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17 results on '"Department of Mathematics [Be'er Sheva]"'

1. Noncommutative Christoffel-Darboux Kernels

Author

Serban Belinschi, Victor Magron, Victor Vinnikov, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Equipe Polynomial OPtimization (LAAS-POP), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Ben-Gurion University of the Negev (BGU), Part of this work was conducted in November 2019 while STB was a visiting fellow supported by the Faculty of Natural Sciences Distinguished Scientist Visitors Program of the Ben Gurion University of the Negev, Beer-Sheva, Israel, and during the three authors’visit at the MFO workshop I.D.: 2010, 'Real Algebraic Geometry with a View Toward Hyperbolic Programming and Free Probability' (1–7 March 2020)., PHC Proteus grant 46195TA, ANR-18-ERC2-0004,COPS,Optimisation garantie pour la vérification des systèmes cyber-physiques(2018), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), European Project: 813211,H2020,POEMA(2019), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Department of Mathematics [Be'er Sheva], Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), Belinschi, Serban, TREMPLIN-ERC - Optimisation garantie pour la vérification des systèmes cyber-physiques - - COPS2018 - ANR-18-ERC2-0004 - TERC - VALID, and Polynomial Optimization, Efficiency through Moments and Algebra - POEMA - - H20202019-01-01 - 2022-12-31 - 813211 - VALID

Subjects
Mathematics - Complex Variables, Mathematics::Complex Variables, Optimization and Control (math.OC), Applied Mathematics, General Mathematics, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], Mathematics - Operator Algebras, FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Complex Variables (math.CV), [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], Operator Algebras (math.OA), Mathematics - Optimization and Control
Abstract

We introduce from an analytic perspective Christoffel-Darboux kernels associated to bounded, tracial noncommutative distributions. We show that properly normalized traces, respectively norms, of evaluations of such kernels on finite dimensional matrices yield classical plurisubharmonic functions as the degree tends to infinity, and show that they are comparable to certain noncommutative versions of the Siciak extremal function. We prove estimates for Siciak functions associated to free products of distributions, and use the classical theory of plurisubharmonic functions in order to propose a notion of support for noncommutative distributions. We conclude with some conjectures and numerical experiments., Comment: 48 pages, 2 figures

Published
2021
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2. About a Non-Standard Interpolation Problem

Author

Alain Yger, Daniel Alpay, Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Institut de Mathématiques de Bordeaux (IMB), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Mathematics - Complex Variables, Applied Mathematics, 010102 general mathematics, Bilinear interpolation, 32A27, 13P, Stairstep interpolation, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], Linear interpolation, Birkhoff interpolation, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Polynomial interpolation, 010101 applied mathematics, Algebra, Computational Theory and Mathematics, Nearest-neighbor interpolation, FOS: Mathematics, Complex Variables (math.CV), 0101 mathematics, Spline interpolation, Analysis, ComputingMilieux_MISCELLANEOUS, Mathematics, Trigonometric interpolation
Abstract

Using algebraic methods, and motivated by the one variable case, we study a multipoint interpolation problem in the setting of several complex variables. The duality realized by the residue generator associated with an underlying Gorenstein algebra, using the Lagrange interpolation polynomial, plays a key role in the arguments.

Published
2018

3. EXPERIMENTAL AND NUMERICAL INVESTIGATION OF WEAK BLAST WAVE INTERACTION WITH A THREE LEVEL BUILDING

Author

Massoni, J, Biamino, L., Jourdan, G, Igra, O, Houas, L, Institut universitaire des systèmes thermiques industriels (IUSTI), Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU), and HOUAS, Lazhar

Subjects
[PHYS]Physics [physics], [SPI]Engineering Sciences [physics], blast reflections, [SPI] Engineering Sciences [physics], human damages, hemic and lymphatic diseases, Astrophysics::High Energy Astrophysical Phenomena, [PHYS.MECA]Physics [physics]/Mechanics [physics], blast enhancement, [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], [SPI.MECA] Engineering Sciences [physics]/Mechanics [physics.med-ph], Blast waves
Abstract

International audience; The present work shows that weak blast waves that are considered as being harmless can turn to become fatal upon their reflections from walls and corners inside a penetrated building. In the experimental part, weak blast waves were generated by using an open-end shock tube. A three level building model was placed in vicinity to the open-end of the used shock tube. The evolved wave pattern inside the building rooms was recorded by a sequence of schlieren photographs; also pressure histories were recorded on the rooms' walls. In addition, numerical simulations of the evolved flow field inside the building was conducted. The good agreement obtained between numerical and experimental results allows running the used code for identifying safety and dangerous places inside the building rooms penetrated by the weak blast wave.

Published
2017

4. Transformée en échelle de signaux stationnaires

Author

Daniel Alpay, Mamadou Mboup, Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804 (CRESTIC), Université de Reims Champagne-Ardenne (URCA), Algebra for Digital Identification and Estimation (ALIEN), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Centrale Lille-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Pure mathematics, Scale (ratio), 010102 general mathematics, Linear system, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], General Medicine, 01 natural sciences, Discrete-time signal, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, 0103 physical sciences, Calculus, 010307 mathematical physics, 0101 mathematics, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Mathematics
Abstract

Scale tranform of discrete stationary signals Using the scale transform of a discrete time signal we define a new family of linear systems. We focus on a particular case related to function theory in the bidisk. To cite this article: D. Alpay, M. Mboup, C. R. Acad. Sci. Paris, Ser. I 347 (2009).

Published
2009

5. Modular representations of GL(n) distinguished by GL(n-1) over a p-adic field

Author

Coolimuttam G. Venketasubramanian, Vincent Sécherre, Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Be'er Sheva], and Ben-Gurion University of the Negev (BGU)

Subjects
Distinguished representations, General Mathematics, Field (mathematics), 01 natural sciences, Combinatorics, Cardinality, Dimension (vector space), Residue field, Gelfand pairs, Linear form, 0103 physical sciences, FOS: Mathematics, Locally compact space, 0101 mathematics, Algebraically closed field, Representation Theory (math.RT), 2010 MSC: 22E50, Mathematics::Representation Theory, Mathematics, [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT], 010102 general mathematics, Modular representations, Irreducible representation, 010307 mathematical physics, p-adic reductive groups, Mathematics - Representation Theory
Abstract

Let $\F$ be a non-Archimedean locally compact field, $q$ be the cardinality of its residue field, and $\R$ be an algebraically closed field of characteristic $\ell$ not dividing $q$.We classify all irredu\-cible smooth $\R$-representations of $\GL\_n(\F)$ having a nonzero $\GL\_{n-1}(\F)$-inva\-riant linear form, when $q$ is not congruent to $1$ mod $\ell$.Partial results in the case when $q$ is $1$ mod $\ell$ show that, unlike the complex case, the space of $\GL\_{n-1}(\F)$-invariant linear forms has dimension $2$ for certain irreducible representations.

Published
2015

6. Geometric density for invariant random subgroups of groups acting on CAT(0) spaces

Author

Nir Lazarovich, Bruno Duchesne, Jean Lécureux, Yair Glasner, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Department of Mathematics (TECHNION), Technion - Israel Institute of Technology [Haifa], Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), and Israel Science Foundation ISF 441/11, U.S. NSF grants DMS 1107452, 1107263, 1107367 'RNMS: Geometric structures And Representation varieties' (the GEAR Network). Région Lorraine

Subjects
Pure mathematics, 20P05, 20F65, 010102 general mathematics, Metric Geometry (math.MG), Group Theory (math.GR), Density theorem, 01 natural sciences, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Mathematics - Metric Geometry, CAT(0) spaces, [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], 0103 physical sciences, FOS: Mathematics, Invariant random subgroups, 010307 mathematical physics, Geometry and Topology, Locally compact space, Geometric density, 0101 mathematics, Invariant (mathematics), Mathematics - Group Theory, [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG], Mathematics
Abstract

International audience; We prove that an IRS of a group with a geometrically dense action on a CAT(0) space also acts geometrically densely; assuming the space is either of finite telescopic dimension or locally compact with finite dimensional Tits boundary. This can be thought of as a Borel density theorem for IRSs.

Published
2014
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7. Dynamique sur l'escalier infini

Author

Barak Weiss, Pascal Hubert, W. Patrick Hooper, Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Laboratoire d'Analyse, Topologie, Probabilités (LATP), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), the City College of New York, Department of mathematics, City College of New York [CUNY] (CCNY), and City University of New York [New York] (CUNY)-City University of New York [New York] (CUNY)

Subjects
Mathematics::Dynamical Systems, Maharam measure, Lebesgue measure, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Ergodicity, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Torus, dynamics, 01 natural sciences, 37D50, 14H30, 30F30, 30F35, 37F30, 0103 physical sciences, infinite staircase, Discrete Mathematics and Combinatorics, Ergodic theory, ergodicity, 010307 mathematical physics, 0101 mathematics, Invariant (mathematics), Analysis, Mathematics, infinite lattice surface
Abstract

The paper is related to the satellite conference on “Various Aspects of Dynamical Systems,” following ICM 2010.; International audience; For the 'infinite staircase' square tiled surface we classify the Radon invariant measures for the straight line flow, obtaining an analogue of the celebrated Veech dichotomy for an infinite genus lattice surface. The ergodic Radon measures arise from Lebesgue measure on a one parameter family of deformations of the surface. The staircase is a ℤ-cover of the torus, reducing the question to the well-studied cylinder map.

Published
2013

8. Almost everywhere convergence of convolution powers on compact Abelian groups

Author

Michael Lin, Jean-Pierre Conze, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Department of mathematics [Israel], and Ben-Gurion University of the Negev ( BGU )

Subjects
Statistics and Probability, Dominated convergence theorem, 60G50, 37A30, 01 natural sciences, Convolution, Combinatorics, 28D05, 47A35, 42A38, 010104 statistics & probability, Convolution powers, Convergence (routing), Almost everywhere, 0101 mathematics, Abelian group, Sweeping out, ComputingMilieux_MISCELLANEOUS, Mathematics, Discrete mathematics, 010102 general mathematics, Almost everywhere convergence, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Strictly aperiodic probabilities, Statistics, Probability and Uncertainty, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Abstract

It is well-known that a probability measure $\mu$ on the circle $\mathbb{T}$ satisfies $\|\mu^{n}*f-\int f\,\mathrm{d}m\|_{p}\to0$ for every $f\in L_{p}$, every (some) $p\in[1,\infty)$, if and only if $|\hat{\mu}(n)|1$. We prove a necessary and sufficient condition, in terms of the Fourier–Stieltjes coefficients of $\mu$, for the strong sweeping out property (existence of a Borel set $B$ with $\limsup\mu^{n}*1_{B}=1$ a.e. and $\liminf\mu^{n}*1_{B}=0$ a.e.). The results are extended to general compact Abelian groups $G$ with Haar measure $m$, and as a corollary we obtain the dichotomy: for $\mu$ strictly aperiodic, either $\mu^{n}*f\to\int f\,\mathrm{d}m$ a.e. for every $p>1$ and every $f\in L_{p}(G,m)$, or $\mu$ has the strong sweeping out property.

Published
2013

9. Ergodicity for Infinite Periodic Translation Surfaces

Author

Pascal Hubert, Barak Weiss, Laboratoire d'Analyse, Topologie, Probabilités (LATP), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Be'er Sheva], and Ben-Gurion University of the Negev (BGU)

Subjects
Mathematics::Dynamical Systems, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], STRIPS, Dynamical Systems (math.DS), 37E35, 01 natural sciences, law.invention, law, Lattice (order), translation surfaces, 0502 economics and business, Translation surface, FOS: Mathematics, Ergodic theory, 0101 mathematics, Mathematics - Dynamical Systems, infinite, Mathematics, Algebra and Number Theory, 010102 general mathematics, 05 social sciences, Ergodicity, Mathematical analysis, periodic, ergodicity, 57S25, 050203 business & management
Abstract

For a $ \mathbb{Z} $-cover $\widetilde {M} \rightarrow M$ of a translation surface, which is a lattice surface, and which admits infinite strips, we prove that almost every direction for the straightline flow is ergodic.

Published
2012

10. Lattice actions on the plane revisited

Author

François Maucourant, Barak Weiss, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Department of mathematics [Israel], Ben-Gurion University of the Negev ( BGU ), Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)

Subjects
Mathematics::Dynamical Systems, [ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR], Hyperbolic geometry, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS], Algebraic geometry, Dynamical Systems (math.DS), Group Theory (math.GR), 01 natural sciences, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], 37A15, Combinatorics, equidistribution, 0502 economics and business, FOS: Mathematics, Ball (mathematics), Mathematics - Dynamical Systems, 0101 mathematics, Mathematics, Projective geometry, Diophantine equation, 010102 general mathematics, 05 social sciences, Lattice, Lie group, Differential geometry, Horocycle, plane, Geometry and Topology, Mathematics - Group Theory, 050203 business & management
Abstract

We study the action of a lattice Γ in the group G = SL(2, R) on the plane. We obtain a formula which simultaneously describes visits of an orbit Γu to either a fixed ball, or an expanding or contracting family of annuli. We also discuss the ‘shrinking target problem’. Our results are valid for an explicitly described set of initial points: all \({{\bf u} \in {\bf R}^2}\) in the case of a cocompact lattice, and all u satisfying certain diophantine conditions in case \({\Gamma = {\rm SL}(2, \mathbb {Z})}\) . The proofs combine the method of Ledrappier with effective equidistribution results for the horocycle flow on \({\Gamma {\backslash} G}\) due to Burger, Strombergsson, Forni and Flaminio.

Published
2012

11. Discrete-time multi-scale systems

Author

Mamadou Mboup, Daniel Alpay, Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804 (CRESTIC), Université de Reims Champagne-Ardenne (URCA), Algebra for Digital Identification and Estimation (ALIEN), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Centrale Lille-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Scale (descriptive set theory), Linear systems, Polydisc, Topology, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Stability (probability), Reproducing kernels, Convolution, Scale invariance, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, FOS: Mathematics, Discrete-scale transformation, 0101 mathematics, Mathematics, Algebra and Number Theory, 010102 general mathematics, Linear system, White noise, 2000 MSC: 94A12, 47N70, 46E22, 93D25, Functional Analysis (math.FA), 010101 applied mathematics, Mathematics - Functional Analysis, Self-similarity, Discrete time and continuous time, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Analysis
Abstract

We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the poly-disc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.

Published
2009

12. A natural transfer function space for linear discrete time-invariant and scale-invariant systems

Author

Daniel Alpay, Mamadou Mboup, Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Université Paris Descartes - UFR de Mathématiques et Informatique (UPD5 Mathématiques Informatique), Université Paris Descartes - Paris 5 (UPD5), Algebra for Digital Identification and Estimation (ALIEN), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Centrale Lille-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Ecole Centrale de Lille-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Department of mathematics [Israel], Ben-Gurion University of the Negev ( BGU ), Université Paris Descartes - UFR de Mathématiques et Informatique ( UPD5 Mathématiques Informatique ), Université Paris Descartes - Paris 5 ( UPD5 ), Algebra for Digital Identification and Estimation ( ALIEN ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique ( Inria ) -Ecole Centrale de Lille-École polytechnique ( X ) -Centre National de la Recherche Scientifique ( CNRS )

Subjects
Pure mathematics, [ INFO.INFO-TS ] Computer Science [cs]/Signal and Image Processing, [ MATH.MATH-CA ] Mathematics [math]/Classical Analysis and ODEs [math.CA], Mathematics::Classical Analysis and ODEs, 02 engineering and technology, [ MATH.MATH-FA ] Mathematics [math]/Functional Analysis [math.FA], [ SPI.SIGNAL ] Engineering Sciences [physics]/Signal and Image processing, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Space (mathematics), [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, symbols.namesake, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Fréchet space, 0202 electrical engineering, electronic engineering, information engineering, Birnbaum–Orlicz space, 0101 mathematics, Lp space, Mathematics, Mathematics::Functional Analysis, Beurling–Lax theorem, Mathematics::Complex Variables, Topological tensor product, 010102 general mathematics, Mathematical analysis, 020206 networking & telecommunications, Hardy space, symbols, Interpolation space, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract

International audience; In a previous work, we have defined the scale shift for a discrete-time signal and introduced a family of linear scale-invariant systems in connection with character-automorphic Hardy spaces. In this paper, we prove a Beurling-Lax theorem for such Hardy spaces of order 2. We also study an interpolation problem in these spaces, as a first step towards a finite dimensional implementation of a scale invariant system. Our approach uses a characterization of character-automorphic Hardy spaces of order 2 in terms of classical de Branges Rovnyak spaces.

Published
2009

13. On the p-adic Beilinson conjecture for number fields

Author

Xavier-François Roblot, Amnon Besser, R.M.H. de Jeu, Paul Buckingham, Roblot, Xavier-François, Geometry, Mathematics, Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Department of Pure Mathematics, University of Sheffield [Sheffield], Faculteit Exacte Wetenschappen Afdeling Wiskunde, Vrije Universiteit Brussel (VUB), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Rational number, Pure mathematics, General Mathematics, Mathematics::Number Theory, Special values, 01 natural sciences, 19F27 (Primary), 11G55, 11R42, 11R70 (Secondary), 0103 physical sciences, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, Abelian group, Mathematics, Discrete mathematics, Conjecture, Mathematics - Number Theory, 010102 general mathematics, K-Theory and Homology (math.KT), State (functional analysis), Artin's conjecture on primitive roots, Algebraic number field, 16. Peace & justice, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Conductor, Mathematics - K-Theory and Homology, 010307 mathematical physics, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Abstract

We formulate a conjectural p-adic analogue of Borel's theorem relating regulators for higher K-groups of number fields to special values of the corresponding zeta-functions, using syntomic regulators and p-adic L-functions. We also formulate a corresponding conjecture for Artin motives, and state a conjecture about the precise relation between the p-adic and classical situations. Parts of he conjectures are proved when the number field (or Artin motive) is Abelian over the rationals, and all conjectures are verified numerically in some other cases., Comment: Improved presentation of p-adic L-functions; added a remark on the compatibility of the signs between the complex and p-adic regulators. To appear in the special volume of the Pure and Applied Math Quarterly on the occasion of the eightieth birthday of Jean-Pierre Serre

Published
2009

14. A characterization of Schur multipliers between character-automorphic Hardy spaces

Author

Mamadou Mboup, Daniel Alpay, Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Université Paris Descartes - UFR de Mathématiques et Informatique (UPD5 Mathématiques Informatique), Université Paris Descartes - Paris 5 (UPD5), Algebra for Digital Identification and Estimation (ALIEN), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Centrale Lille-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Ecole Centrale de Lille-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Department of mathematics [Israel], Ben-Gurion University of the Negev ( BGU ), Université Paris Descartes - UFR de Mathématiques et Informatique ( UPD5 Mathématiques Informatique ), Université Paris Descartes - Paris 5 ( UPD5 ), Algebra for Digital Identification and Estimation ( ALIEN ), Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique ( Inria ) -Ecole Centrale de Lille-École polytechnique ( X ) -Centre National de la Recherche Scientifique ( CNRS )

Subjects
[ MATH.MATH-CV ] Mathematics [math]/Complex Variables [math.CV], Pure mathematics, [ INFO.INFO-TS ] Computer Science [cs]/Signal and Image Processing, [ SPI.SIGNAL ] Engineering Sciences [physics]/Signal and Image processing, 02 engineering and technology, Characterization (mathematics), 01 natural sciences, symbols.namesake, Character-automorphiuc functions, Factorization, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, 0101 mathematics, Complex Variables (math.CV), Mathematics, Schur multipliers, Mathematics::Functional Analysis, Algebra and Number Theory, Hardy spaces, Mathematics - Complex Variables, Mathematics::Complex Variables, 010102 general mathematics, de Branges Rovnyak spaces, Order (ring theory), 020206 networking & telecommunications, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], Extension (predicate logic), Hardy space, Algebra, Character (mathematics), symbols, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Analysis, Analytic function
Abstract

International audience; We give a new characterization of character-automorphic Hardy spaces of order $2$ and of their contractive multipliers in terms of de Branges Rovnyak spaces. Keys tools in our arguments are analytic extension and a factorization result for matrix-valued analytic functions due to Leech.

Published
2008
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15. Bounds on the trace mapping of LD-fields

Author

Reuven Segev, Ronen Peretz, Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Department of Mechanical Engineering [Beer-Sheva], and Cardillo, Christian

Subjects
Trace (linear algebra), Boundary (topology), Context (language use), 02 engineering and technology, [SPI.MECA] Engineering Sciences [physics]/Mechanics [physics.med-ph], Space (mathematics), 01 natural sciences, Stress (mechanics), 0203 mechanical engineering, Bounds, Modelling and Simulation, 0101 mathematics, Mathematics, Stress concentration, Continuum mechanics, 010102 general mathematics, Mathematical analysis, [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], 16. Peace & justice, Sobolev space, Computational Mathematics, 020303 mechanical engineering & transports, Computational Theory and Mathematics, Modeling and Simulation, Trace
Abstract

International audience; Bounds on the trace mappings defined on the Sobolev space View the MathML sourceW^{1,1}(Ω) and the space LD(Ω) of integrable strains are obtained. In the mechanics of continuous media, such bounds correspond to stress concentration--the ratio between the maximal stress in a body and the maximum of the traction applied to its boundary. The analysis leading to the bounds may be described in the mechanical context of stress theory and stress concentration.

Published
2007

16. Combinatorial Dominance Guarantees for Heuristic Algorithms

Author

Daniel Berend, Yochai Twitto, Steven Skiena, Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Department of Computer Science [Beer-Sheva], Computer Science Department [SUNY], Stony Brook University [SUNY] (SBU), State University of New York (SUNY)-State University of New York (SUNY), and Jacquet, Philippe

Subjects
Optimization problem, General Computer Science, Domination analysis, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], 0211 other engineering and technologies, Vertex cover, [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS], 0102 computer and information sciences, 02 engineering and technology, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, Theoretical Computer Science, Combinatorics, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Discrete Mathematics and Combinatorics, approximation algorithms, Mathematics, 021103 operations research, Heuristic, Approximation algorithm, Set cover problem, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG], 010201 computation theory & mathematics, Knapsack problem, Combinatorial optimization, combinatorial optimization, domination analysis, Algorithm
Abstract

An $f(n)$ $\textit{dominance bound}$ on a heuristic for some problem is a guarantee that the heuristic always returns a solution not worse than at least $f(n)$ solutions. In this paper, we analyze several heuristics for $\textit{Vertex Cover}$, $\textit{Set Cover}$, and $\textit{Knapsack}$ for dominance bounds. In particular, we show that the well-known $\textit{maximal matching}$ heuristic of $\textit{Vertex Cover}$ provides an excellent dominance bound. We introduce new general analysis techniques which apply to a wide range of problems and heuristics for this measure. Certain general results relating approximation ratio and combinatorial dominance guarantees for optimization problems over subsets are established. We prove certain limitations on the combinatorial dominance guarantees of polynomial-time approximation schemes (PTAS), and give inapproximability results for the problems above.

Published
2007

17. Convex hull for intersections of random lines

Author

Vladimir Braverman, Daniel Berend, Department of Mathematics [Be'er Sheva], Ben-Gurion University of the Negev (BGU), Department of Electrical Engineering [New York], Columbia University [New York], and Conrado Martínez

Subjects
Convex hull, General Computer Science, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], random lines, Theoretical Computer Science, Combinatorics, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Range (mathematics), [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], Intersection, [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Discrete Mathematics and Combinatorics, [INFO.INFO-HC]Computer Science [cs]/Human-Computer Interaction [cs.HC], [INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC], Algorithm, Time complexity, convex hull, Mathematics
Abstract

The problem of finding the convex hull of the intersection points of random lines was studied in Devroye and Toussaint, 1993 and Langerman, Golin and Steiger, 2002, and algorithms with expected linear time were found. We improve the previous results of the model in Devroye and Toussaint, 1993 by giving a universal algorithm for a wider range of distributions.

Published
2005

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