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Inspired by recent developments in the theory of Banach and operator algebras of locally compact groups, we construct several new classes of bifunctors (A,B)\mapsto A\otimes _{\alpha } B, where A\otimes _\alpha B is a cross norm completion of A\odot B for each pair of C*-algebras A and B. For the first class of bifunctors considered (A,B)\mapsto A{\otimes _p} B (1\leq p\leq \infty), A{\otimes _p} B is a Banach algebra cross-norm completion of A\odot B constructed in a fashion similar to p-pseudofunctions \text {PF}^*_p(G) of a locally compact group. Taking a cue from the recently introduced symmetrized p-pseudofunctions due to Liao and Yu and later by the second and the third named authors, we also consider {\otimes _{p,q}} for Hölder conjugate p,q\in [1,\infty ] – a Banach *-algebra analogue of the tensor product {\otimes _{p,q}}. By taking enveloping C*-algebras of A{\otimes _{p,q}} B, we arrive at a third bifunctor (A,B)\mapsto A{\otimes _{\mathrm C^*_{p,q}}} B where the resulting algebra A{\otimes _{\mathrm C^*_{p,q}}} B is a C*-algebra. For G_1 and G_2 belonging to a large class of discrete groups, we show that the tensor products \mathrm C^*_{\mathrm r}(G_1){\otimes _{\mathrm C^*_{p,q}}}\mathrm C^*_{\mathrm r}(G_2) coincide with a Brown-Guentner type C*-completion of \mathrm \ell ^1(G_1\times G_2) and conclude that if 2\leq p'

The occasion for this survey article was the 70th birthday of Jan Stochel, professor at Jagiellonian University, former head of the Chair of Functional Analysis and a prominent member of the Kraków school of operator theory. In the course of his mathematical career, he has dealt, among other things, with various aspects of functional analysis, single and multivariable operator theory, the theory of moments, the theory of orthogonal polynomials, the theory of reproducing kernel Hilbert spaces, and mathematical aspects of quantum mechanics. [ABSTRACT FROM AUTHOR]

Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of certain set-valued mappings between function spaces. This paper deals with the computational properties of these accretive and (generalized) monotone set-valued operators. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie "non-computational" proofs from the mainstream literature. To this end, we establish logical metatheorems that guarantee and quantify the computational content of theorems pertaining to accretive and (generalized) monotone set-valued operators. On the one hand, our results unify a number of recent case studies, while they also provide characterizations of central analytical notions in terms of proof theoretic ones on the other, which provides a crucial perspective on needed quantitative assumptions in future applications of proof mining to these branches. [ABSTRACT FROM AUTHOR]

Convex functions and their analogues have been powerful tools in almost all mathematical fields, including optimization, fractional calculus, mathematical analysis, functional analysis, operator theory, and mathematical physics. It is well established in the literature that a convex function f : [0,∞) → [0,∞) with f(0) = 0 is necessarily superadditive, while a concave function f : [0,∞) → [0,∞) is subadditive. The converses of these two assertions are not valid in general. The main target of this article is to study the subadditivity and superadditivity of convex and superquadratic functions. In particular, we obtain several results extending, refining, and reversing some known inequalities in this direction. Further discussion of superquadratic functions in this line will be given. [ABSTRACT FROM AUTHOR]

We address an open problem in ensemble control: Whether there exist controllable linear ensemble systems over multidimensional parameterization spaces? We provide a negative result: Any real-analytic linear ensemble system is not Lp-controllable, for 2≤ p≤\infty, if its parameterization space contains an open set in Rd for d ≥2. [ABSTRACT FROM AUTHOR]

This paper concerns a nonhomogeneous singular fractional order system, with two frictional damping terms. This system can be considered as a generalization of the so-called Timoshenko system. Results on the existence, uniqueness, and continuous dependence on the solution were obtained via an energy approach, which mainly relies on a priori bounds and density arguments. The approach relies on functional analysis tools and operator theory. Very few results concerning the well-posedness of fractional order Timoshenko systems can be found in the literature. Our results generalize and improve the previous ones and significantly boost the development of the used method. [ABSTRACT FROM AUTHOR]

We are devoted to the study of a non-local non-homogeneous time fractional Timoshenko system with frictional and viscoelastic damping terms. We are concerned with the well-posedness of the given problem. The approach relies on some functional analysis tools, operator theory, a priori estimates and density arguments. This work can be considered as a contribution to the development of energy inequality methods, the so-called a priori estimate method inspired from functional analyses and used to prove the well-posedness of mixed problems with integral boundary conditions. [ABSTRACT FROM AUTHOR]

Recent advances in operator learning theory have improved our knowledge about learning maps between infinite dimensional spaces. However, for large-scale engineering problems such as concurrent multiscale simulation for mechanical properties, the training cost for current deep learning methods is high and unscalable. The article presents a thorough analysis on the mathematical underpinnings of the operator learning paradigm and proposes a kernel learning method that maps between Banach spaces of functions. We first provide a survey of modern kernel and operator learning theory, as well as discuss recent results and open problems. From there, the article presents an algorithm to show we can analytically approximate the piecewise constant functions on R for operator learning. This implies the potential feasibility of success of neural operators on clustered functions, at least on the real line. Finally, a k-means clustered domain on the basis of a mechanistic response is considered and the Lippmann-Schwinger equation for micro-mechanical homogenization is solved. The article briefly discusses the mathematics of previous kernel learning methods and some preliminary results with those methods. The proposed kernel operator learning method uses graph kernel networks to come up with a mechanistic reduced order method for multiscale homogenization. [ABSTRACT FROM AUTHOR]

This paper presents new results related to Bombieri's generalization of Bessel's inequality in a semi-inner product space induced by a positive semidefinite operator A. Specifically, we establish new inequalities that generalize the classical Bessel inequality and extend previous results in this area. Furthermore, our findings have applications to the study of operators on positive semidefinite inner product spaces, also known as semi-Hilbert spaces, and contribute to a deeper understanding of their properties and applications. Our work has implications for various fields, including functional analysis and operator theory. [ABSTRACT FROM AUTHOR]

The category LAlg of L-algebras is shown to be complete and cocomplete, regular with a zero object and a projective generator, normal and subtractive, ideal determined, but not Barr-exact. Originating from algebraic logic, L-algebras arise in the theory of Garside groups, measure theory, functional analysis, and operator theory. It is shown that the category LAlg is far from protomodular, but it has natural semidirect products which have not been described in category-theoretic terms. [ABSTRACT FROM AUTHOR]

A quadratic stochastic operator (QSO) is frequently acknowledged as the analysis source to investigate dynamical properties and modeling in numerous areas. Countless classes of QSO have been investigated since the operator was introduced in 1920s. The study of QSOs is still an open problem in the nonlinear operator theory field, especially QSOs on infinite state space. We are interested in the dynamics of Geometric QSO generated by a 2-partition defined on countable state space. We first show the system of equations formed from defined Geometric QSO with infinite-dimensional space can be simplified into a one-dimensional setting, corresponding to the number of defined partitions. The trajectory behavior of such a system is investigated by using functional analysis approach, where the operator either converges to a unique fixed point or has a second-order cycle. It is shown that such an operator can be either regular or nonregular for arbitrary initial points depending on the value of parameters. In this research, we present two cases, i.e., two different parameters and three different parameters. We display the form of the fixed point and periodic points of period-2. Moreover, an example for the nonregular transformation will be provided, where such QSO has 2-periodic points. [ABSTRACT FROM AUTHOR]

In this paper, we characterize spaces of L ∞ -functions on a compact Hausdorff space that are invariant under a transitive and continuous group action. This work is analogous to established results concerning invariant spaces of continuous and measurable functions on a compact Hausdorff space. The case for L ∞ -functions cannot be proved in the same way when endowed with the norm-topology, but a similar argument can be used when the space of L ∞ -functions is given the weak*-topology, as we show in this paper. [ABSTRACT FROM AUTHOR]

The design of optimal Magnetic Resonance Imaging (MRI) coils is modeled as a minimum-norm problem (MNP), that is, as an optimization problem of the form min x ∈ R ∥ x ∥ , where R is a closed and convex subset of a normed space X. This manuscript is aimed at revisiting MNPs from the perspective of Functional Analysis, Operator Theory, and Banach Space Geometry in order to provide an analytic solution to the following MRI problem: min ψ ∈ R ∥ ψ ∥ 2 , where R : = { ψ ∈ R n : ∥ A ψ − b ∥ ∞ ∥ b ∥ ∞ ≤ D } , with A ∈ M m × n (R) , D > 0 , and b ∈ R m ∖ { 0 } . [ABSTRACT FROM AUTHOR]

The present work addresses some new controllability results for a class of fractional integrodifferential dynamical systems with a delay in Banach spaces. Under the new definition of controllability, first introduced by us, we obtain some sufficient conditions of controllability for the considered dynamic systems. To conquer the difficulties arising from time delay, we also introduce a suitable delay item in a special complete space. In this work, a nonlinear item is not assumed to have Lipschitz continuity or other growth hypotheses compared with most existing articles. Our main tools are resolvent operator theory and fixed point theory. At last, an example is presented to explain our abstract conclusions. [ABSTRACT FROM AUTHOR]

Capacities of quantum channels and decoherence times both quantify the extent to which quantum information can withstand degradation by interactions with its environment. However, calculating capacities directly is known to be intractable in general. Much recent work has focused on upper bounding certain capacities in terms of more tractable quantities such as specific norms from operator theory. In the meantime, there has also been substantial recent progress on estimating decoherence times with techniques from analysis and geometry, even though many hard questions remain open. In this article, we introduce a class of continuous-time quantum channels that we called transferred channels, which are built through representation theory from a classical Markov kernel defined on a compact group. In particular, we study two subclasses of such kernels: Hörmander systems on compact Lie-groups and Markov chains on finite groups. Examples of transferred channels include the depolarizing channel, the dephasing channel, and collective decoherence channels acting on d qubits. Some of the estimates presented are new, such as those for channels that randomly swap subsystems. We then extend tools developed in earlier work by Gao, Junge and LaRacuente to transfer estimates of the classical Markov kernel to the transferred channels and study in this way different non-commutative functional inequalities. The main contribution of this article is the application of this transference principle to the estimation of decoherence time, of private and quantum capacities, of entanglement-assisted classical capacities as well as estimation of entanglement breaking times, defined as the first time for which the channel becomes entanglement breaking. Moreover, our estimates hold for non-ergodic channels such as the collective decoherence channels, an important scenario that has been overlooked so far because of a lack of techniques. [ABSTRACT FROM AUTHOR]

By using the method of functional analysis, especially C 0 -semigroup theory and spectral theory of linear operators we prove the well-posedness and the existence of a unique positive dynamic solution of a deteriorating system with multiple vacations of a repairman. Moreover, we show spectral properties of the system operator which imply that the system does not have a steady-state solution. [ABSTRACT FROM AUTHOR]

The paper discusses the influence of new geometric invariants of domains on Hessian integral inequalities and provides a new proof of the well-known Trudinger–Wang inequalities. A comparative analysis of the Trudinger–Wang inequalities with the classical Poincaré–Friedrichs inequality is carried out; it shows that these inequalities are qualitatively different. It is shown that Hessian integral inequalities contain information of new type and have no analogues in classical functional analysis. [ABSTRACT FROM AUTHOR]

The object of the present paper is to obtain subordination, superordination and sandwich-type results related to a certain family of integral operators defined on the space of multivalent functions in the open unit disk. Also we point out relevant connections of the results presented here with those obtained in earlier. [ABSTRACT FROM AUTHOR]

We generalize some inequalities for positive unital linear map as follows: Let A, B be positive operators on a Hilbert space with 0 < m ≤ A ≥ m' < M' ≤ B ≤ M. Then for every positive unital linear map Φ, μ ∊ [0; 1] and p > 0, Φ p(A Δμ B+2rMm(A-1ΔB-1-A-1#ΔB-1))≤αp Φ p(A#μB) and Φ p(A Δμ B+2rMm(A-1ΔB-1-A-1#ΔB-1))≤αp(Φ(A)#αΦ(B))p where r = min{μ,1-μ}, h'=M'/m' and α=max{(M+m)2/4MmK(√h',2)R,(M+m)2/42/pMmK(√h',2)R}. Fur- thermore, we give a squaring reversed Karcher mean inequality involving positive linear map. [ABSTRACT FROM AUTHOR]

In this paper we have introduced and studied the subclass L(λ, d, α, β) using the fractional integral as- sociated with the convolution product of Sălăgean operator and Ruscheweyh derivative. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neigh- borhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class L(λ, d, α, β). [ABSTRACT FROM AUTHOR]

In this paper, we construct a generalization of Durrmeyer type Baskakov operators based on the concept of (p, q)-integers and bivariate tensor product form. For the univariate case, we obtain the estimates of moments and central moments of these operators, establish a local approximation theorem, obtain the estimates on the rate of convergence and weighted approximation of those operators. For the bivariate case, we give the rate of convergence by using the weighted modulus of continuity, give some graphs and numerical examples to illustrate the convergent properties of these operators to certain functions. We also compare these operators Dn,p,q with another forms. [ABSTRACT FROM AUTHOR]

In this paper we establish some equalities and inequalities for K-g-frames. Our results generalize the remarkable results obtained by Balan et al. and Găvruţa. We also give several new inequalities for K-g-frames by using operator theory methods, which differ in structure from those for frames. [ABSTRACT FROM AUTHOR]

We present a suitable framework for the definition of quantum time delay in terms of sojourn times for unitary operators in a two-Hilbert spaces setting. We prove that this time delay defined in terms of sojourn times (time-dependent definition) exists and coincides with the expectation value of a unitary analogue of the Eisenbud–Wigner time delay operator (time-independent definition). Our proofs rely on a new summation formula relating localization operators to time operators and on various tools from functional analysis such as Mackey's imprimitivity theorem, Trotter–Kato formula and commutator methods for unitary operators. Our approach is general and model-independent. [ABSTRACT FROM AUTHOR]

The description of the nuclear magnetic resonance magnetization dynamics in the presence of long-range dipolar interactions, which is based upon approximate solutions of Bloch–Torrey equations including the effect of a distant dipolar field, has been revisited. New experiments show that approximate analytic solutions have a broader regime of validity as well as dependencies on pulse-sequence parameters that seem to have been overlooked. In order to explain these experimental results, we developed a new method consisting of calculating the magnetization via an iterative formalism where both diffusion and distant dipolar field contributions are treated as integral operators incorporated into the Bloch–Torrey equations. The solution can be organized as a perturbative series, whereby access to higher order terms allows one to set better boundaries on validity regimes for analytic first-order approximations. Finally, the method legitimizes the use of simple analytic first-order approximations under less demanding experimental conditions, it predicts new pulse-sequence parameter dependencies for the range of validity, and clarifies weak points in previous calculations. [ABSTRACT FROM AUTHOR]

Both formal and numerical analyses have been carried out on various exact and approximate variants of the four-component relativistic theory for nuclear magnetic shielding constants. These include the standard linear response theory (LRT), the full or external field-dependent unitary transformations of the Dirac operator, as well as the orbital decomposition approach. In contrast with LRT, the latter schemes take explicitly into account both the kinetic and magnetic balances between the large and small components of the Dirac spinors, and are therefore much less demanding on the basis sets. In addition, the diamagnetic contributions, which are otherwise “missing” in LRT, appear naturally in the latter schemes. Nevertheless, the definitions of paramagnetic and diamagnetic terms are not the same in the different schemes, but the difference is only of O(c-2) and thus vanishes in the nonrelativistic limit. It is shown that, as an operator theory, the full field-dependent unitary transformation approach cannot be applied to singular magnetic fields such as that due to the magnetic point dipole moment of a nucleus. However, the inherent singularities can be avoided by the corresponding matrix formulation (with a partial closed summation). All the schemes are combined with the Dirac-Kohn-Sham ansatz for ground state calculations, and by using virtually complete basis sets a new and more accurate set of absolute nuclear magnetic resonance shielding scales for the rare gases He–Rn have been established. [ABSTRACT FROM AUTHOR]

This paper compares harmonic and anharmonic zero-point energies and thermodynamic functions for a number of molecules of small and medium size. Anharmonic corrections cannot be neglected for quantitative studies, but can be obtained quite effectively by a perturbative treatment including cubic force constants to the second order and semidiagonal quartic constants to the first order. Simple finite difference equations provide all the necessary terms by at most 6N-11 Hessian evaluations, where N is the number of atoms in the system. Accurate values are obtained by this method using the Becke three parameter Lee–Yang–Parr functional, medium size basis sets, and, when needed, proper treatment of internal rotations. The whole model has been completely automated in the Gaussian package. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Abstract We study some "almost preserver" problems on von Neumann algebra modules. More precisely, we study (1) maps which "almost preserve" the right or left annihilator; (2) the "almost band preservers" – that is, maps which "almost preserve corners", and (3) "almost centralizers," which almost preserve module actions. Under certain conditions, we show that maps of these types are automatically continuous, and can be approximated by maps which precisely preserve these relations; often, the operators from the latter class are multiplication operators. [ABSTRACT FROM AUTHOR]

Abstract Given a monotone function f ∈ C r [ − 1 , 1 ] , r ≥ 1 , we obtain pointwise estimates for its monotone approximation by piecewise polynomials involving the second order modulus of smoothness of f (r) . These estimates are interpolatory estimates, namely, the piecewise polynomials interpolate the function at the endpoints of the interval. However, they are valid only for n ≥ N (f , r). We also show that such estimates are in general invalid with N independent of f. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the boundedness and compactness of weighted composition operators from Zygmund-type spaces to weighted-type spaces and little weighted-type spaces in the unit ball of Cn. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study the connection between the spectral condition of an Hermite subdivision operator and polynomial reproduction properties of the associated subdivision scheme. While it is known that in general the spectral condition does not imply the reproduction of polynomials, we here prove that a special spectral condition (defined by shifted monomials) is actually equivalent to the reproduction of polynomials. We further put into evidence that the sum rule of order ℓ > d associated with an Hermite subdivision operator of order d does not imply that the spectral condition of order ℓ is satisfied, while it is known that these two concepts are equivalent in the case ℓ = d. Highlights • Certain spectral and polynomial reproduction properties of Hermite schemes are equivalent. • High order sum rules do not imply spectral conditions of the same order. • Polynomial generation implies spectral conditions. [ABSTRACT FROM AUTHOR]

In this paper we establish some equalities and inequalities for K-g-frames. Our results generalize the remarkable results obtained by Balan et al. and Găvruţa. We also give several new inequalities for K-g-frames by using operator theory methods, which differ in structure from those for frames. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of infinitely many solutions of the following degenerate magnetic fractional problem involving critical Sobolev‐Hardy nonlinearities: M([u]s,A2)(−△)Asu=λf(x,|u|)u+|u|2s∗(α)−2u|x|α,inRN,where s ∈ (0,1), N > 2s, 2s∗(α)=2(N−α)N−2s is the fractional Hardy‐Sobolev critical exponent with α ∈ [0,2s), λ is a positive real parameter, M:R0+→R0+ is a Kirchhoff function, A:RN→RN is a magnetic potential function, and (−△)As is the fractional magnetic operator. By using the new version of symmetric mountain pass theorem of Kajikiya, we prove that the problem admits infinitely many solutions for the suitable value of λ. [ABSTRACT FROM AUTHOR]

We introduce the algebraic Heun operator associated to any bispectral pair of operators. This operator can be presented as a generic bilinear combination of these bispectral operators. We show that the resulting operators are natural generalizations of the ordinary Heun operator. This leads to a simple construction of the operators commuting with the projection operators in problems of band-time limiting and it gives a way to adapt a construction first used by Perline in a purely finite setup to general situations. We also extend this algebraic construction to cover some purely finite cases which lie beyond this scheme, in particular for the anti-Krawtchouk polynomials. In the latter case, the commuting operator is represented by a pentadiagonal matrix which can be constructed explicitly as a polynomial of degree 4 of the pair of bispectral operators. [ABSTRACT FROM AUTHOR]

We study how the shelling components behave under the pyramid and prism operations. As a consequence we obtain a concise recursion for the cubical shelling contributions. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to give a new formula of the joint spectral radius of commuting d -tuples of operators on a complex Hilbert space. Also we show that r ( T ) ≤ ω ( T ) for a commuting d -tuple of operators T , where r ( T ) and ω ( T ) denote respectively the joint spectral radius and the joint numerical radius of T . This generalizes the well known relation between the spectral and the numerical radii of Hilbert space operators which is proved in [10] . [ABSTRACT FROM AUTHOR]

New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space. [ABSTRACT FROM AUTHOR]

We study the Dirichlet problem in a domain with a small hole close to the boundary. To do so, for each pair ε = ( ε 1 , ε 2 ) of positive parameters, we consider a perforated domain Ω ε obtained by making a small hole of size ε 1 ε 2 in an open regular subset Ω of R n at distance ε 1 from the boundary ∂Ω. As ε 1 → 0 , the perforation shrinks to a point and, at the same time, approaches the boundary. When ε → ( 0 , 0 ) , the size of the hole shrinks at a faster rate than its approach to the boundary. We denote by u ε the solution of a Dirichlet problem for the Laplace equation in Ω ε . For a space dimension n ≥ 3 , we show that the function mapping ε to u ε has a real analytic continuation in a neighborhood of ( 0 , 0 ) . By contrast, for n = 2 we consider two different regimes: ε tends to ( 0 , 0 ) , and ε 1 tends to 0 with ε 2 fixed. When ε → ( 0 , 0 ) , the solution u ε has a logarithmic behavior; when only ε 1 → 0 and ε 2 is fixed, the asymptotic behavior of the solution can be described in terms of real analytic functions of ε 1 . We also show that for n = 2 , the energy integral and the total flux on the exterior boundary have different limiting values in the two regimes. We prove these results by using functional analysis methods in conjunction with certain special layer potentials. [ABSTRACT FROM AUTHOR]

Many aggregation operators in multiattribute decisions assume that attributes are independent of each other; this leads to an unreasonable situation in information aggregation and decision-making. Heronian mean is the aggregation operator that can embody the interaction between attributes. In this paper, we merge the linguistic neutrosophic cubic number (LNCN) and the Heronian mean operator together to develop a LNCN generalized weighted Heronian mean (LNCNGWHM) operator and a LNCN three-parameter weighted Heronian mean (LNCNTPWHM) operator and then discuss their properties. Further, two multiattribute decision methods based on the proposed LNCNGWHM or LNCNTPWHM operator are introduced under LNCN environment. Finally, an example is used to indicate the effectiveness of the developed methods. [ABSTRACT FROM AUTHOR]

The present paper deals with a generalization of the Baskakov operators. Some direct theorems, asymptotic formula and A-statistical convergence are established. Our results are based on a ρ function. These results include the preservation properties of the classical Baskakov operators. [ABSTRACT FROM AUTHOR]

Let K be a nonempty convex subset of a real Banach space X. Let T be a nearly weak uniformly L-Lipschitzian mapping. A modified Mann-type iteration scheme is proved to converge strongly to the unique fixed point of T. Our result is a significant improvement and generalization of several known results in this area of research. We give a specific example to support our result. Furthermore, an interesting equivalence of T-stability result between the convergence of modified Mann-type and modified Mann iterations is included. [ABSTRACT FROM AUTHOR]

We present an improved version of Young's inequality as well as an operator inequality version of it. Our result is compared to the latest refinements. [ABSTRACT FROM AUTHOR]

Recently, a new functional analytic construction of quasi-free states for a self-dual CAR algebra has been presented in Finster and Reintjes (Adv Theor Math Phys 20:1007, 2016). This method relies on the so-called strong mass oscillation property. We provide an example where this requirement is not satisfied, due to the nonvanishing trace of the solutions of the Dirac equation on the horizon of Rindler space, and we propose a modification of the construction in order to weaken this condition. Finally, a connection between the two approaches is built. [ABSTRACT FROM AUTHOR]

Assuming only strong stabilizability, we construct the maximal solution of the algebraic Riccati equation as the strong limit of a Kleinman–Newton sequence of bounded nonnegative operators. As a corollary we obtain a comparison of the solutions of two algebraic Riccati equations associated with different cost functions. We show that the weaker strong stabilizability assumptions are satisfied by partial differential systems with collocated actuators and sensors, so the results have potential applications to numerical approximations of such systems. By means of a counterexample, we illustrate that even if one assumes exponential stabilizability, the Kleinman–Newton construction may provide a solution to the Riccati equation that is not strongly stabilizing. [ABSTRACT FROM AUTHOR]

Following an idea of Lin, we prove that if A and B are two positive operators such that 0 < mI ≤ A ≤ m′ I ≤ M′ I ≤ B ≤ MI, then and where $$K\left( h \right) = \frac{{{{\left( {h + 1} \right)}^2}}}{{4h}}$$ and $$h = \frac{M}{m}$$ and Φ is a positive unital linear map. [ABSTRACT FROM AUTHOR]

Most methods for analyzing functional time series rely on the estimation of lagged autocovariance operators or surfaces. As in univariate time series analysis, testing whether or not such operators are zero is an important diagnostic step that is well understood when the data, or model residuals, form a strong white noise. When functional data are constructed from dense records of, for example, asset prices or returns, a weak white noise model allowing for conditional heteroscedasticity is often more realistic. Applying inferential procedures for the autocovariance based on a strong white noise to such data often leads to the erroneous conclusion that the data exhibit significant autocorrelation. We develop methods for performing inference for the lagged autocovariance operators of stationary functional time series that are valid under general conditional heteroscedasticity conditions. These include a portmanteau test to assess the cumulative significance of empirical autocovariance operators up to a user selected maximum lag, as well as methods for obtaining confidence bands for a functional version of the autocorrelation that are useful in model selection/validation. We analyze the efficacy of these methods through a simulation study, and apply them to functional time series derived from asset price data of several representative assets. In this application, we found that strong white noise tests often suggest that such series exhibit significant autocorrelation, whereas our tests, which account for functional conditional heteroscedasticity, show that these data are in fact uncorrelated in a function space. [ABSTRACT FROM AUTHOR]

In this article,we show the stability of the doubly Feller property of the resolvent for Markov processes, generalizing a work by Kai-Lai Chung on the stability of the doubly Feller property of a semigroup with multiplicative functionals. The stability of the doubly Feller property of the resolvent under time change is also presented. [ABSTRACT FROM AUTHOR]

In this paper we show that the transfer operator of a Rauzy-Veech-Zorich renormalization map acting on a space of quasi-Hölder functions is quasicompact and derive certain statistical recurrence properties for this map and its associated Teichmüller flow. We establish Borel-Cantelli lemmas, Extreme Value statistics and return time statistics for the map and flow. Previous results have established quasicompactness in Hölder or analytic function spaces, for example the work of M. Pollicott and T. Morita. The quasi-Hölder function space is particularly useful for investigating return time statistics. In particular we establish the shrinking target property for nested balls in the setting of Teichmüller flow. Our point of view, approach and terminology derive from the work of M. Pollicott augmented by that of M. Viana. [ABSTRACT FROM AUTHOR]

We characterize the K-functional K ˜ ψ ( f , t ) p (used in approximating functions by Durrmeyer and Kantorovich modifications of Baskakov operator) K ˜ ψ ( f , t ) p = inf ⁡ { ‖ f − g ‖ p + t ‖ D ˜ g ‖ p : f − g ∈ L p [ 0 , ∞ ) , g ∈ W ˜ p [ 0 , ∞ ) } where D ˜ = d d x ( x ( 1 + x ) d d x ) , W ˜ p [ 0 , ∞ ) = { f : f , f ′ ∈ A C l o c ( 0 , ∞ ) , D ˜ f ∈ L p [ 0 , ∞ ) , lim x → 0 + , ∞ ⁡ ψ ( x ) f ′ ( x ) = 0 } by appropriate moduli of smoothness. [ABSTRACT FROM AUTHOR]