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We give sufficient conditions for a BL-algebra to be isomorphic to a poset product of BL-chains which are poset product indecomposable. Fil: Busaniche, Manuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Gomez, Conrado Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina

Let G be an LCA group, H a closed subgroup, Γ the dual group of G and µ be a regular finite non-negative Borel measureonΓ. Motivated by the problem of sampling and reconstruction of a stationary random process over G from the values of m different linear measurements on H, we give some necessary or sufficient conditions for the density of certain sets of functions inL2(µ), which arise in multichannel sampling. Extensions of these results toLp(µ) , p≠ 2, and the existence of unconditional convergent expansions are discussed. Fil: Lutz , Peter Klotz. Universitat Leipzig; Alemania Fil: Medina, Juan Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; Argentina

Consider an operator A :H→K between Hilbert spaces and closed subspaces S ⊂ H and T ⊂ K. If there exist projections E on H and F on K such that R(E) =S, R(F) =T and AE=F∗A then A is called (S, T)-complementable. The origin of this notion comes from the idea of T. Ando of defining Schur complements in terms of operators. In this paper we present some characterizations of these triples (A, S, T) and applications to bilateral Schur complements and generalized Wiener-Hopf operators. Fil: Arias, Maria Laura. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina Fil: Maestripieri, Alejandra Laura. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina

Let $G$ be a compact connected semisimple Lie group, let $K$ be a closed subgroup of $G$, let $\Gamma$ be a finite subgroup of $G$, and let $\tau$ be a finite-dimensional representation of $K$. For $\pi$ in the unitary dual $\widehat G$ of $G$, denote by $n_\Gamma(\pi)$ its multiplicity in $L^2(\Gamma\backslash G)$. We prove a strong multiplicity one theorem in the spirit of Bhagwat and Rajan, for the $n_\Gamma(\pi)$ for $\pi$ in the set $\widehat G_\tau$ of irreducible $\tau$-spherical representations of $G$. More precisely, for $\Gamma$ and $\Gamma'$ finite subgroups of $G$, we prove that if $n_{\Gamma}(\pi)= n_{\Gamma'}(\pi)$ for all but finitely many $\pi\in \widehat G_\tau$, then $\Gamma$ and $\Gamma'$ are $\tau$-representation equivalent, that is, $n_{\Gamma}(\pi)=n_{\Gamma'}(\pi)$ for all $\pi\in \widehat G_\tau$. Moreover, when $\widehat G_\tau$ can be written as a finite union of strings of representations, we prove a finite version of the above result. For any finite subset $\widehat {F}_{\tau}$ of $\widehat G_{\tau}$ verifying some mild conditions, the values of the $n_\Gamma(\pi)$ for $\pi\in\widehat F_{\tau}$ determine the $n_\Gamma(\pi)$'s for all $\pi \in \widehat G_\tau$. In particular, for two finite subgroups $\Gamma$ and $\Gamma'$ of $G$, if $n_\Gamma(\pi) = n_{\Gamma'}(\pi)$ for all $\pi\in \widehat F_{\tau}$ then the equality holds for every $\pi \in \widehat G_\tau$. We use algebraic methods involving generating functions and some facts from the representation theory of $G$., Comment: Final version, to appear in Proc. AMS

We study the existence of Gabor orthonormal bases with window the characteristic function of the set Ω = [ 0 , α ] ∪ [ β + α , β + 1 ] of measure 1, with α , β > 0 . By the symmetries of the problem, we can restrict our attention to the case α ≤ 1 / 2 . We prove that either if α 1 / 2 or ( α = 1 / 2 and β ≥ 1 / 2 ) there exist such Gabor orthonormal bases, with window the characteristic function of the set Ω, if and only if Ω tiles the line. Furthermore, in both cases, we completely describe the structure of the set of time–frequency shifts associated to these bases., Departamento de Matemática

We study certain pairs of subspaces V and W of C^n we call supports that consist of eigenspaces of the eigenvalues ±‖M‖ of a minimal hermitian matrix M(‖M‖ ≤‖M+D‖ for all real diagonals D). For any pair of orthogonal subspaces we define a non negative invariant δ called the adequacy to measure how close they are to form a support and to detect one. This function δ is the minimum of another map F defined in a product of spheres of hermitian matrices. We study the gradient, Hessian and critical points of F in order to approximate δ. These results allow us to prove that the set of supports has interior points in the space of flag manifolds. Fil: Mendoza, Alberto. Universidad Simón Bolívar; Venezuela Fil: Recht, Lázaro. Universidad Simón Bolívar; Venezuela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina Fil: Varela, Alejandro. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina

We characterize the weights for the Stieltjes transform and the Calder´on operator to be bounded on the weighted variable Lebesgue spaces $L_w^{p(cdot)}(0,infty)$, assuming that the exponent function $pp$ is log-H"older continuous at the origin and at infinity. We obtain a single Muckenhoupt-type condition by means of a maximal operator defined with respect to the basis of intervals ${ (0,b) : b>0}$ on $(0,infty)$. Our results extend those in cite{DMRO1} for the constant exponent $L^p$ spaces with weights. We also give two applications: the first is a weighted version of Hilbert´s inequality on variable Lebesgue spaces, and the second generalizes the results in cite{SW} for integral operators to the variable exponent setting. Fil: Cruz-Uribe, David. University Of Alabama; Fil: Dalmasso, Estefanía Dafne. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Martín Reyes, Francisco Javier. Universidad de Málaga. Facultad de Ciencias; España Fil: Ortega Salvador, Pedro. Universidad de Málaga. Facultad de Ciencias; España

Let $S\in\mathcal{M}_d(\mathbb{C})^+$ be a positive semidefinite $d\times d$ complex matrix and let $\mathbf a=(a_i)_{i\in\mathbb{I}_k}\in \mathbb{R}_{>0}^k$, indexed by $\mathbb{I}_k=\{1,\ldots,k\}$, be a $k$-tuple of positive numbers. Let $\mathbb T_{d}(\mathbf a )$ denote the set of families $\mathcal G=\{g_i\}_{i\in\mathbb{I}_k}\in (\mathbb{C}^d)^k$ such that $\|g_i\|^2=a_i$, for $i\in\mathbb{I}_k$; thus, $\mathbb T_{d}(\mathbf a )$ is the product of spheres in $\mathbb{C}^d$ endowed with the product metric. For a strictly convex unitarily invariant norm $N$ in $\mathcal{M}_d(\mathbb{C})$, we consider the generalized frame operator distance function $\Theta_{( N \, , \, S\, , \, \mathbf a)}$ defined on $\mathbb T_{d}(\mathbf a )$, given by $$ \Theta_{( N \, , \, S\, , \, \mathbf a)}(\mathcal G) =N(S-S_{\mathcal G }) \quad \text{where} \quad S_{\mathcal G}=\sum_{i\in\mathbb{I}_k} g_i\,g_i^*\in\mathcal{M}_d(\mathbb{C})^+\,. $$ In this paper we determine the geometrical and spectral structure of local minimizers $\mathcal G_0\in\mathbb T_{d}(\mathbf a )$ of $\Theta_{( N \, , \, S\, , \, \mathbf a)}$. In particular, we show that local minimizers are global minimizers, and that these families do not depend on the particular choice of $N$., Comment: 24 pages. There exists text overlap with other arxiv manuscripts in the preliminary sections

Se trabajó en aspectos teóricos y computacionales de formas de Hilbert de peso medio entero, en particular el problema de la base y fórmulas tipo Waldspurger. Específicamente se desarrollararon métodos para la construcción de formas de Hilbert de peso medio entero estudiada por Xue y Sirolli al mayor nivel de generalidad posible, demostrando una fórmula explícita tipo Waldspurger. Se realizaron progresos significativos en el desarrollo de capacidades de investigación fundamental en Teoría de números y el fortalecimiento de los vínculos regionales e internacionales, con especial énfasis en la formación de jóvenes investigadores y la consolidación de un grupo de investigación nacional en Teoría de Números. En el marco del proyecto se desarrollóuna escuela de investigación sobre curvas elípticas para estudiantes de posgrado de la región, contando con la visita de importantes científicos provenientes de Francia, Italia y Holanda. Página de la escuela: http://www.rnta.eu/Montevideo2019/ Aprovechando la oportunidad de la escuela organizamos, en colaboración con el programa Pelota al Medio a la Esperanza del Ministerio del Interior, una actividad para estudiantes de secundaria en el Espacio Avanza de Antel. El Profesor Fernando Rodriguez-Villegas (ICTP, Trieste) dictó una charla de divulgación titulada "Matemáticas y fútbol" que se encuentra disponible en: http://veramas.com.uy/veramas/vod/40292/795 Agencia Nacional de Investigación e Innovación

Fil: Bottazzi, Tamara Paula. Universidad Nacional de Río Negro. Centro Interdisciplinario de Telecomunicaciones, Electrónica, Computación y Ciencia Aplicada. Río Negro, Argentina. . Si X es el conjunto de operadores compactos o p-Schatten sobre un espacio de Hilbert complejo separable H, estudiamos la existencia y caracterización de operadores Hermitianos A ∈ X tales que |||A||| ≤ |||A + D|||, para todo D ∈ D(X ), o equivalentemente |||A||| = min |||A + D||| = dist (A, D(X )) , D∈D(X ) siendo D(X ) el subespacio de operadores diagonales de X en alguna base prefijada de H y ||| · ||| es la norma usual de operadores en cada X . Usamos la ortogonalidad Birkhoff-James como herramienta para caracterizar y desarrollar propiedades de dichos operadores en cada contexto. También proveemos diversos ejemplos muy ilustrativos.

Este proyecto pretende avanzar la comprensión del estudio de objetos que poseen ciertas estructuras geométricas. En muchos casos, estas estructuras geométricas pueden ser testeadas a nivel local pero tienen implicancias fuertes a nivel global. Esta relativamente reciente constatación permitió explicar ciertos fenómenos que se observan desde hace mucho tiempo y da lugar a pensar que es algo que se encuentra detrás de otros fenómenos aún mal comprendidos. Recientemente, el estudio de la geometría se ha visto beneficiado por la incorporación de técnicas de sistemas dinámicos (y en caso también probabilidad) y este es el camino que buscamos en este proyecto. Agencia Nacional de Investigación e Innovación

Let A be a unital C*-algebra. Given a faithful representation A⊂B(L) in a Hilbert space L, the set G^+⊂A of positive invertible elements can be thought of as the set of inner products in L, related to A, which are equivalent to the original inner product. The set G^+ has a rich geometry, it is a homogeneous space of the invertible group G of A, with an invariant Finsler metric. In the present paper we study the tangent bundle TG^+ of G^+, as a homogenous Finsler space of a natural group of invertible matrices in M_2(A), identifying TG^+ with the it Poincaré half-space H of A. H={H ∈ A : Im(h)≥ 0,Im(h) invertible}. We show that H≃TG^+ has properties similar to those of a space of non-positive constant curvature. Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Simon Bolivar.; Venezuela

The notion of covering type was recently introduced by Karoubi and Weibel to measure the complexity of a topological space by means of good coverings. When X has the homotopy type of a finite CW-complex, its covering type coincides with the minimum possible number of vertices of a simplicial complex homotopy equivalent to X. In this article we compute the covering type of all closed surfaces. Our results completely settle a problem posed by Karoubi and Weibel, and shed more light on the relationship between the topology of surfaces and the number of vertices of minimal triangulations from a homotopy point of view., 6 pages

Generalizing the method of Faltings–Serre, we rigorously verify that certain abelian surfaces without extra endomorphisms are paramodular. To compute the required Hecke eigenvalues, we develop a method of specialization of Siegel paramodular forms to modular curves. Fil: Brumer, Armand. Fordham University; Estados Unidos Fil: Pacetti, Ariel Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina Fil: Poor, Cris. Fordham University; Estados Unidos Fil: Tornaría, Gonzalo. Universidad de la República; Uruguay Fil: Voight, John. Dartmouth College; Estados Unidos Fil: Yuen, David S.. University of Hawaii; Estados Unidos

For a proper open set $Omega$ immersed in a metric space with the weak homogeneity property, and given a measure $mu$ doubling on a certain family of balls lying ``well inside´´ of $Omega$, we introduce local operators of singular and fractional type and study their boundedness properties on weighted $L^p(Omega)$, $1leq p < infty$, for weights in local Muckenhoupt classes. Fil: Harboure, Eleonor Ofelia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Salinas, Oscar Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Viviani, Beatriz Eleonora. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina

The use of Haar wavelet analysis, instead of classical trigonometric analysis, provides inequalities which can be regarded as Heisenberg-type inequalities associated to fractional order quantum mechanics. The aim of this paper is to introduce and prove some of these lower order uncertainty estimates. Fil: Aimar, Hugo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Bolcatto, Pablo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Gomez, Ivana Daniela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina

We investigate a stronger formulation of Webb's conjecture on the contractibilty of the orbit space of the p-subgroup complexes in terms of finite topological spaces. The original conjecture, which was first proved by Symonds and, more recently, by Bux, Libman and Linckelmann, can be restated in terms of the topology of certain finite spaces. We propose a stronger conjecture, and prove various particular cases by combining fusion theory of finite groups and homotopy theory of finite spaces., Comment: 21 pages

We combine dyadic analysis through Haar type wavelets defined on Christ's families of generalized cubes, and Lax-Milgram theorem, in order to prove existence of Green's functions for fractional Laplacians on some function spaces of vanishing small resolution in spaces of homogeneous type., 10 pages

We prove that if $\mathfrak{s}$ is a solvable Lie algebra of matrices over a field of characteristic 0 and $A\in \mathfrak{s}$ , then the semisimple and nilpotent summands of the Jordan–Chevalley decomposition of $A$ belong to $\mathfrak{s}$ if and only if there exist $S,N\in \mathfrak{s}$ , $S$ is semisimple, $N$ is nilpotent (not necessarily $[S,N]=0$ ) such that $A=S+N$ .

In this work we analyze a nonlinear eigenvalue problem for the p-Laplacian operator with zero Dirichlet boundary conditions. We assume that the problem has a potential which depends on the eigenvalue parameter, and we show that, for n big enough, there exists a real eigenvalue λn, and their corresponding eigenfunctions have exactly n nodal domains. We characterize the asymptotic behavior of these eigenvalues, obtaining two terms in the asymptotic expansion of λn in powers of n. Finally, we study the inverse nodal problem in the case of energy dependent potentials, showing that some subset of the zeros of the corresponding eigenfunctions is enough to determine the main term of the potential. Fil: Koyunbakan, Hikmet. Firat Universitesi; Turquía Fil: Pinasco, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina Fil: Scarola, Cristian. Universidad Nacional de la Pampa. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

Given a finite dimensional algebra over a perfect field the text introduces covering functors over the mesh category of any modulated Auslander-Reiten component of the algebra. This is applied to study the composition of irreducible morphisms between indecomposable modules in relation with the powers of the radical of the module category., Minor modifications. Final version to appear in the Journal of Pure and Applied Algebra

An algebra $\mathbf A = \langle A, \to, 0 \rangle$, where $\to$ is binary and $0$ is a constant, is called an implication zroupoid ($\mathcal I$-zroupoid, for short) if $\mathbf A$ satisfies the identities: $(x \to y) \to z \approx ((z' \to x) \to (y \to z)')'$ and $0'' \approx 0$, where $x' : = x \to 0$. An implication zroupoid is symmetric if it satisfies $x'' \approx x$ and $(x \to y')' \approx (y \to x')'$. The variety of symmetric $\mathcal I$-zroupoids is denoted by $\mathcal S$. We began a systematic analysis of weak associative laws of length $\leq 4$ in [CS16e], by examining the identities of Bol-Moufang type in the context of the variety $\mathcal S$. In this paper we complete the analysis by investigating the rest of the weak associative laws of length $\leq 4$ relative to $\mathcal S$. We show that, of the 155 subvarieties of $\mathcal S$ defined by the weak associative laws of size $\leq 4$, there are exactly $6$ distinct ones. We also give an explicit description of the poset of the (distinct) subvarieties of $\mathcal S$ defined by weak associative laws of length $\leq 4$., 36 pages

We prove that a generalized Fefferman-Phong type condition on a pair of weights $u$ and $v$ is sufficient for the boundedness of the commutators of potential type operators from $L^{p(\cdot)}_v$ into $L^{q(\cdot)}_u$. We also give an improvement of this result in the sense that we not only consider a variable version of power bump conditions, but also weaker norms related to Musielak-Orlicz functions. We consider a wider class of symbols including Lipschitz symbols and some generalizations., Comment: 29 pages

The main goal of this work is to prove the existence of three different solutions (one positive, one negative and one with nonconstant sign) for the equation $(-\Delta_p)^s u= |u|^{p^{*}_s -2} u +\lambda f(x,u)$ in a bounded domain with Dirichlet condition, where $(-\Delta_p)^s$ is the well known $p$-fractional Laplacian and $p^*_s=\frac{np}{n-sp}$ is the critical Sobolev exponent for the non local case. The proof is based in the extension of the Concentration Compactness Principle for the $p$-fractional Laplacian and Ekeland's variational Principle., Comment: 10 pages. arXiv admin note: text overlap with arXiv:0808.3143, arXiv:0912.3465

In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main result of the paper sentences that under different conditions on the weights we can obtain $$\Bigg\| \frac{T(\vec f\,)(x)}{v}\Bigg\|_{L^{\frac{1}{m}, \infty}(\nu v^\frac{1}{m})} \leq C \ \prod_{i=1}^m{\|f_i\|_{L^1(w_i)}}, $$ where $T$ is a multilinear Calder\'on-Zygmund operator. To obtain this result we first prove it for the $m$-fold product of the Hardy-Littlewood maximal operator $M$, and also for $\mathcal{M}(\vec{f})(x)$: the multi(sub)linear maximal function introduced in \cite{LOPTT}. As an application we also prove a vector-valued extension to the mixed weighted weak-type inequalities of multilinear Calder\'on-Zygmund operators., Comment: 10 pages

We study the pairs of projections PIf=χIf,QJf=(χJf) ˇ, f∈L^2(R^n), where I,J⊂R^n are sets of finite positive Lebesgue measure, χI,χJ denote the corresponding characteristic functions and ˇ, ˇ denote the Fourier-Plancherel transformation L^2(R^n)→L^2(R^n) and its inverse. These pairs of projections have been widely studied by several authors in connection with the mathematical formulation of Heisenberg´s uncertainty principle. Our study is done from a differential geometric point of view. We apply known results on the Finsler geometry of the Grassmann manifold P(H) of a Hilbert space H to establish that there exists a unique minimal geodesic of P(L^2(R^n)), which is a curve of the δ(t)=e^{itXI,J}P^{Ie−itXI,J} which joins PI and QJ and has length π/2. Here X_I,J is a selfadjoint operator determined by the sets I,J. As a consequence we deduce that if H is the logarithm of the Fourier-Plancherel map, then ∥[H,PI]∥≥π/2. The spectrum of X_I,J is denumerable and symmetric with respect to the origin, and it has a smallest positive eigenvalue γ(X_I,J) which satisfies cos(γ(X_I,J))=∥PIQJ∥. Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina

In this article we study the hypercyclic behavior of non-convolution operators defined on spaces of analytic functions of different holomorphy types over Banach spaces. The operators in the family we analyze are a composition of differentiation and composition operators, and are extensions of operators in H(C) studied by Aron and Markose in 2004. The dynamics of this class of operators, in the context of one and several complex variables, was further investigated by many authors. It turns out that the situation is somewhat different and that some purely infinite dimensional difficulties appear. For example, in contrast to the several complex variable case, it may happen that the symbol of the composition operator has no fixed points and still, the operator is not hypercyclic. We also prove a Runge type theorem for holomorphy types on Banach spaces. Fil: Muro, Luis Santiago Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina Fil: Pinasco, Damian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Torcuato Di Tella. Departamento de Matemáticas y Estadística; Argentina Fil: Savransky, Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina

Let ${\cal E}$ be a topos, ${\rm{Dec}}\left( {\cal E} \right) \to {\cal E}$ be the full subcategory of decidable objects, and ${{\cal E}_{\neg \,\,\neg }} \to {\cal E}$ be the full subcategory of double-negation sheaves. We give sufficient conditions for the existence of a Unity and Identity ${\cal E} \to {\cal S}$ for the two subcategories of ${\cal E}$ above, making them Adjointly Opposite. Typical examples of such ${\cal E}$ include many ‘gros’ toposes in Algebraic Geometry, simplicial sets and other toposes of ‘combinatorial’ spaces in Algebraic Topology, and certain models of Synthetic Differential Geometry.

In the study of the spectra of algebras of holomorphic functions on a Banach space E, the bidual E″ has a central role, and the spectrum is often shown to be locally homeomorphic to E″. In this paper we consider the problem of spectra of subalgebras invariant under the action of a group (functions f such that f ○ g = f). It is natural to attempt a characterization in terms of the space of orbits E″/~ obtained from E″ through the action of the group, so we pursue this approach here and introduce an analytic structure on the spectrum in some situations. In other situations we encounter some obstacles: in some cases, the lack of structure of E″/~ itself; in others, problems of weak continuity and non-approximability of functions in the algebra. We also define a convolution operation related to the spectrum.

We present a reduction theory for first-order Lagrangian field theories which takes into account the conservation of momenta. The relation between the solutions of the original problem with a prescribed value of the momentum and the solutions of the reduced problem is established. An illustrative example is discussed in detail. Fil: Capriotti, Santiago. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina Fil: García-Toraño Andrés, Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina

We derive a description of the family of canonical selfadjoint extensions of the operator of multiplication in a de Branges space in terms of singular rank-one perturbations using distinguished elements from the set of functions associated with a de Branges space. The scale of rigged Hilbert spaces associated with this construction is also studied from the viewpoint of de Branges's theory., 26 pages no figures. Typos corrected. Some remarks and an example added

Lidskii's additive inequalities (both for eigenvalues and singular values) can be interpreted as an explicit description of global minimizers of functions that are built on unitarily invariant norms, with domains consisting of certain orbits of matrices (under the action of the unitary group). In this paper, we show that Lidskii's inequalities actually describe all global minimizers of such functions and that local minimizers are also global minimizers. We use these results to obtain partial results related to local minimizers of generalized frame operator distances in the context of finite frame theory., Facultad de Ciencias Exactas

In this article, we obtain explicit approximations of the modified error function introduced in Cho and Sunderland (1974), as part of a Stefan problem with a temperature-dependent thermal conductivity. This function depends on a parameter δ which is related to the thermal conductivity in the original phase-change process. We propose a method to obtain approximations, which is based on the assumption that the modified error function admits a power series representation in δ. Accurate approximations are obtained through functions involving error and exponential functions only. For the special case in which δ assumes small positive values, we show that the modified error function presents some characteristic features of the classical error function, such as monotony, concavity, and boundedness. Moreover, we prove that the modified error function converges to the classical one when δ goes to zero. Fil: Ceretani, Andrea Noemí. Universidad Austral. Facultad de Ciencias Empresariales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina Fil: Salva, Natalia Nieves. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Universidad Nacional del Comahue; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral. Facultad de Ciencias Empresariales; Argentina

In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {→, ∧, ⊤}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses. Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina Fil: Menchón, María Paula. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

In this paper we deal with anomalous diffusions induced by Continuous Time Random Walks - CTRW in $\mathbb{R}^n$. A particle moves in $\mathbb{R}^n$ in such a way that the probability density function $u(\cdot,t)$ of finding it in region $\Omega$ of $\mathbb{R}^n$ is given by $\int_{\Omega}u(x,t) dx$. The dynamics of the diffusion is provided by a space time probability density $J(x,t)$ compactly supported in $\{t\geq 0\}$. For $t$ large enough, $u$ must satisfy the equation $u(x,t)=[(J-\delta)\ast u](x,t)$ where $\delta$ is the Dirac delta in space time. We give a sense to a Cauchy type problem for a given initial density distribution $f$. We use Banach fixed point method to solve it, and we prove that under parabolic rescaling of $J$ the equation tends weakly to the heat equation and that for particular kernels $J$ the solutions tend to the corresponding temperatures when the scaling parameter approaches to zero., Comment: 15 pages, 2 figures. We added a proof that T^m_1 f is continuous as a function of t with values in L^1(R^n) in page 9. Second version has been accepted for publication on Journal d'Analyse Math\'ematique (June 2015)

Let $E$ be a rational elliptic curve and let $p$ be an odd prime of additive reduction. Let $K$ be an imaginary quadratic field and fix a positive integer $c$ prime to the conductor of $E$. The main goal of the present article is to define an anticyclotomic $p$-adic $L$-function $\L$ attached to $E/K$ when $E/\QQ_p$ attains semistable reduction over an abelian extension. We prove that $\L$ satisfies the expected interpolation properties; namely, we show that if $\chi$ is an anticyclotomic character of conductor $cp^n$ then $\chi(\L)$ is equal (up to explicit constants) to $L(E,\chi,1)$ or $L'(E,\chi,1)$., Comment: 17 pages, to appear in Comptes rendus - Math\'ematique

We prove that a finite non-degenerate involutive set-theoretic solution (X,r) of the Yang-Baxter equation is a multipermutation solution if and only if its structure group G(X,r) admits a left ordering or equivalently it is poly-(infinite cyclic)., Comment: 7 pages

Fil: Bottazzi, Tamara Paula. Universidad Nacional de Río Negro. CITECCA. Río Negro, Argentina. Fil: Bottazzi, Tamara Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Buenos Aires, Argentina. Fil: Conde. Cristian Marcelo. Instituto Argentino de Matemática “Alberto P. Calderón”. Buenos Aires, Argentina. Fil: Conde. Cristian Marcelo. Universidad Nacional de Gral. Sarmiento. Instituto de Ciencias. Buenos Aires, Argentina In [2], Abu Omar and Kittaneh defined a new generalization of the numerical radius. That is, given a norm N (·) on B(H), the space of bounded linear operators over a Hilbert space H, and A ∈ B(H) w N (A) = sup N (Re(e iθ A)). θ∈R They proved several properties and introduced some inequalities. We continue with the study of this generalized numerical radius and we develop diverse inequalities involving w N . We also study particular cases when N (·) is the p- Schatten norm with p > 1. En 2019, Abu Omar y Kittaneh definieron una nueva generaliación del radio numérico. Esta es, dada una norma N (·) sobre B(H), el espacio de los operadores lineales y acotados que actúan sobre un espacio de Hilbert H, y A ∈ B(H) w N (A) = sup N (Re(e iθ A)). θ∈R Nosotros continuamos con el estudio de este radio numérico generalizado y desarrollamos diversas desigualdades involucrándolo. También estudiamos casos particulares en los que la norma N (·) es la de tipo p- Schatten con p > 1.

Let $\mu$ be a probability measure on $\mathbb{T}$ that is singular with respect to the Haar measure. In this paper we study Fourier expansions in $L^2(\mathbb{T},\mu)$ using techniques from the theory of model subspaces of the Hardy space. Since the sequence of monomials $\{z^n\}_{n\in \mathbb{N}}$ is effective in $L^2(\mathbb{T},\mu)$, it has a Parseval frame associated via the Kaczmarz algorithm. Our first main goal is to identify the aforementioned frame with boundary values of the frame $P_\varphi(z^n)$ for the model subspace $\mathcal{H}(\varphi)= H^2 \ominus \varphi H^2$, where $P_\varphi$ is the orthogonal projection from the Hardy space $H^2$ onto $\mathcal{H}(\varphi)$. The study of Fourier expansions in $L^2(\mathbb{T},\mu)$ also leads to consider positive kernels in the Hardy space. Our second main goal is to study the set of measures $\mu$ which reproduce a kernel contained in a model subspace. We completely characterize this set when the kernel is the reproducing kernel of a model subspace, and we study the consequences of this characterization., Comment: 19 pages

In this paper we solve a long standing problem about the multivariable Rubio de Francia extrapolation theorem for the multilinear Muckenhoupt classes A, which were extensively studied by Lerner et al. and which are the natural ones for the class of multilinear Calderón-Zygmund operators as well as for some bilinear rough singular integral operators. Furthermore, we go beyond the classes A and extrapolate within the classes A which appear naturally associated to the weighted norm inequalities for multilinear sparse forms which control fundamental operators such as the bilinear Hilbert transform. We give several applications which can be easily obtained using extrapolation. First, weighted norm inequalities (scalar and vector-valued) for the bilinear rough singular integral operators are established. Second, for the bilinear Hilbert transform one can extrapolate from the recent result of Culiuc et al. who considered the Banach range, extend the estimates to the quasi-Banach range, and furthermore, prove trivially vector-valued inequalities. We also extend recent results of Carando et al. on Marcinkiewicz-Zygmund estimates for multilinear Calderón-Zygmund operators. Finally, our last application gives new weighted estimates (scalar and vector-valued) for the commutators of multilinear Calderón-Zygmund operators, bilinear rough singular integral operators, and for the bilinear Hilbert transform with BMO functions using ideas from Bényi et al., The first author is supported by Juan de la Cierva - Formación 2015 FJCI-2015-24547, by the Basque Government through the BERC 2018-2021 program and by Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and through project MTM2017-82160-C2-1-P funded by (AEI/FEDER, UE) and acronym “HAQMEC”. The second author acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa” Programme for Centres of Excellence in R&D” (SEV-2015-0554). He also acknowledges that the research leading to these results has received funding from the European Research Council under the European Union Seventh Framework Programme (FP7/2007-2013)/ERC agreement no. 615112 HAPDEGMT. The third author is supported by CONICET PIP 11220130100329CO, Argentina, by the Basque Government through the BERC 2018-2021 program and by Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation SEV-2013-0323

In this paper we give quantitative bounds for the norms of different kinds of singular integral operators on weighted Hardy spaces Hpw, where 0 < p ≤ 1 and w is a weight in the Muckenhoupt A∞ class. We deal with Fourier multiplier operators, Calderon–Zygmund operators of homogeneous type which are particular cases of the first ones, and, more generally, we study singular integrals of convolution type. In order to prove mixed estimates in the setting of weighted Hardy spaces, we need to introduce several characterizations of weighted Hardy spaces by means of square functions, Littlewood–Paley functions and the grand maximal function. We also establish explicit quantitative bounds depending on the weight w when switching between the Hpw-norms defined by the Littlewood–Paley–Stein square function and its discrete version, and also by applying the mixed bound Aq–A∞ result for the vector-valued extension of the Hardy–Littlewood maximal operator given in Buckley (Trans Am Math Soc 340(1):253–272, 1993)., Facultad de Ciencias Exactas

In this article we prove dimension free $L^p$?boundedness of Riesz transforms associated with a Bessel differential operator. We obtain explicit estimates of the $L^p$?norms for the Bessel?Riesz transforms in terms of $p$, establishing a linear behavior with respect to $p$. We use the Bellman function technique to prove a bilinear dimension free inequality involving Poisson semigroups defined through this Bessel operator. Fil: Betancor, Jorge J.. Universidad de la Laguna. Departamento de Analisis Matematico; España Fil: Dalmasso, Estefanía Dafne. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Fariña, Juan C.. Universidad de la Laguna. Departamento de Analisis Matematico; España Fil: Scotto, Roberto Aníbal. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina

In this paper we introduce variable exponent local Hardy spaces $hLp$ associated with a non-negative self-adjoint operator $L$. We assume that, for every $t>0$, the operator $e^{-tL}$ has an integral representation whose kernel satisfies a Gaussian upper bound. We define $hLp$ by using an area square integral involving the semigroup ${e^{-tL}}_{t>0}$. A molecular characterization of $hLp$ is established. As an application of the molecular characterization we prove that $hLp$ coincides with the (global) Hardy space $HLp$ provided that $0$ does not belong to the spectrum of $L$. Also, we show that $hLp=H_{L+I}^{p(cdot)}(mathbb R^n)$. Fil: Almeida, Víctor. Universidad de la Laguna. Departamento de Analisis Matematico; España Fil: Betancor, Jorge J.. Universidad de la Laguna. Departamento de Analisis Matematico; España Fil: Dalmasso, Estefanía Dafne. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Rodríguez-Mesa, Lourdes. Universidad de la Laguna. Departamento de Analisis Matematico; España

In this paper we study the continuous dynamical sampling problem at infinite time in a complex Hilbert space H. We find necessary and sufficient conditions on a bounded linear operator A∈B(H) and a set of vectors G⊂H, in order to obtain that {etAg}g∈G,t∈[0,∞) is a semi-continuous frame for H. We study if it is possible to discretize the time variable t and still have a frame for H. We also relate the continuous iteration etA on a set G to the discrete iteration (A′)n on G′ for an adequate operator A′ and set G′⊂H. Fil: Díaz Martín, Rocío Patricia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina Fil: Medri, Ivan Vladimir. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Molter, Ursula Maria. No especifíca

In this article, we address the problem of reconstructing an element in a Hilbert space from its samples by means of a weighted least square approximation. We show how this problem is linked with the notions of weighted inverses, weighted projections and an angle condition known as compatibility. In addition, we study perfect reconstruction operators and their relationship with the previous problem. Finally, since the reconstructions through these approaches may not be unique, we propose different criteria for choosing an optimal one among all of them. Fil: Arias, Maria Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina Fil: Gonzalez, Maria Celeste. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina