Interpolation in Spaces of Analytic Functions
Interpolation dans les espaces de fonctions analytiques
18 – 22 November 2019
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Scientific Committee
Comité scientifique Aline Bonami (Université d’Orléans) |
Organizing Committee
Comité d’organisation Emmanuel Fricain (Université de Lille) |
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The goal of this conference is to gather people interested in holomorphic interpolation and related subjects, including sampling theory, uniqueness problems, and reproducing kernel Hilbert spaces. Related results and methods from this area of research play a fundamental role in different branches of modern analysis. For example, Carleson’s well-known characterization of interpolating sequences in the algebra of bounded analytic functions in the unit disk and the subsequent solution of the corona problem were groundbreaking results and continue to generate activity in analysis.
In the Hilbertian situation, interpolation, uniqueness, and sampling translate to geometric properties of reproducing kernels. After orthonormal sequences, Riesz sequences of such kernels (which are related to interpolation) represent the second best family one can expect in a Hilbert space. Riesz sequences, and their complete counterpart, Riesz bases, are fundamental elements contributing not only to a better understanding of the underlying Hilbert spaces, but playing a central role in operator theory and its applications, such as signal processing, mathematical physics, and machine learning. We are particularly interested in the use of Riesz bases in control theory. We also note that in the last decade spectacular progress was made when a number of longstanding open problems were solved (e.g., the Kadison-Singer conjecture and the completeness problem for biorthogonal exponentials). |
L’objectif de cette conférence est de réunir des experts autour de problèmes d’interpolation, d’échantillonnage et d’unicité. Ces problèmes jouent un rôle fondamental dans diverses branches de l’analyse moderne. Le célèbre théorème de Carleson concernant la description des suites d’interpolation dans l’algèbre des fonctions holomorphes bornées dans le disque unité et la résolution du problème de la couronne représentaient des progrès majeurs dans la compréhension de cette algèbre et continuent `a engendrer de nouvelles questions importante dans cette direction.
Dans le cadre hilbertien, interpolation, unicité, échantillonnage etc. se traduisent par des propriétés géométriques des suites de noyaux reproduisants. Les bases de Riesz (correspondant aux suites d’interpolation complètes) sont presque comme des bases orthonormales : les coefficients sur la base définissent toujours une norme équivalente. Les suites et bases de Riesz permettent non seulement de mieux comprendre la structure des espaces de Hilbert en question, mais elles jouent également un rôle central dans les applications (théorie du signal, physique mathématiques, machine learning,…). Un intérêt particulier de la conférence concernera l’utilisation des bases de Riesz en théorie du contrôle. Notons que pendant cette dernière décennie, des progrès spectaculaires ont été réalisés dans de nombreux problèmes liés (p.ex., la conjecture de Kadison-Singer et le problème de complétude de la biorthogonale associée à une famille minimale et complète d’exponentielles). |
Araft Abbar (Université Paris-Est Marne-la-Vallée) Γ-Supercyclicity for strongly continuous semigroups
Eric Amar (Université Bordeaux 1) Interpolating sequences and Carleson measures in Hardy spaces of the polydisc. Some new results
Hafid Bahajji-el Idrissi (Université Mohammed-V, Rabat) Blaschke products and zero sets in weighted Dirichlet spaces
Anton Baranov (HSE Campus in St. Petersburg) Nearly invariant subspaces in spaces of entire functions
Kelly Bickel (Bucknell University Pennsylvania) Rational inner functions and their Zero Set Behavior
José Bonet (Polytechnic University of Valencia) Solid hulls and cores of weighted H∞-spaces
Alexander Borichev (Aix-Marseille Université) The Szegö minimum problem
Marcin Bownik (University of Oregon) Exponential frames and syndetic Riesz sequences
Isabelle Chalendar (Université Paris-Est Marne-la-Vallée) In Koenigs’ footsteps: diagonalization of composition operators
Nikolaos Chalmoukis (University of Bologna) Random interpolation for the Dirichlet space
Vikramjeet Singh Chandel (Indian Institute of Technology Bombay) The 3-point spectral Pick interpolation problem
Raphaël Clouatre (University of Manitoba) When is a complete Nevanlinna–Pick quotient a function algebra?
Alberto Dayan (Washington University in St Louis) Interpolating Matrices
Michael Dritschel (Newcastle University) The rational dilation problem on distinguished varieties
Jean Esterle (Université Bordeaux 1) Do some z-invariant subspaces have the division property?
Stephen Farnham (Syracuse University) laschke decompositions on weighted Hardy spaces
Eva A. Gallardo-Gutiérrez (Complutense University of Madrid) Spectral decompositions and an extension of a Theorem of Atzmon: a couple leading to spectral subspaces for Bishop operators
Walton Green (Clemson University) The uncertainty principle in control theory
Sophie Grivaux (CNRS/Université de Lille) Rigidity sequences, Kazhdan sets and group topologies on the integers
Michael Hartz (FernUniversität in Hagen) Pick and peak interpolation in function spaces on the ball
Friedrich Haslinger (University of Vienna) The ∂-complex on the Segal-Bargmann space
Birgit Jacob (BUW Wuppertal) Stability and well-posedness of boundary control systems
Karim Kellay (Université de Bordeaux) Riesz bases of reproducing kernels in small Fock spaces
Stanislas Kupin (Université de Bordeaux) Lieb-Thirring inequalities for an effective Hamiltonian of bilayer graphene
Eddy Kwessi (Trinity University) The special atom space in higher dimensions
Constanze Liaw (University of Delaware) Singular parts of matrix-valued Aleksandrov-Clark Measures
Shuaibing Luo (Hunan University) Expansive operators and invariant subspaces of the de Branges-Rovnyak spaces
Zinaida Lykova (Newcastle University) Interpolation problems for analytic functions from the unit disc to the tetrablock
Javad Mashreghi (Université de Laval) Constructive approximation methods in super harmonically weighted Dirichlet spaces
John E. McCarthy (Washington University St Louis)
Norm-preserving extensions of bounded holomorphic functions
Mishko Mitkovski (Clemson University) Uncertainty principles of Logvinenko-Sereda-Paneah type
Artur Nicolau (UAB Barcelona)
Shahaf Nitzan (Georgia Institute of Technology) TBA
Jan-Fredrik Olsen (Lund University) On local properties of function spaces of Dirichlet series
Marcu-Antone Orsoni (Université de Bordeaux) Reachable space of the heat equation and holo- morphic function spaces
Joaquim Ortega-Cerdà (UB Barcelona) Strict density inequalities for interpolation in weighted spaces of holomorphic functions in several complex variables
Caleb Parks (University of Arkansas) Interpolation in analytic tent spaces
José A. Peláez (University of Málaga) The dual of the Bergman space of A1ω
Sandra Pott (Lund University) Commutators and matrix weights in finite and infinite dimensions
Thomas Ransford (Université de Laval) Constructive polynomial approximation in Banach spaces of holomorphic functions
Oliver Roth (University of Würzburg) A Schwarz lemma for locally univalent meromorphic functions
Eskil Rydhe (University of Leeds & University of Lund) On Laplace–Carleson embeddings
Felix Schwenninger (University of Hamburg) H∞ calculus and control: new and old
Kristian Seip (Norwegian University of Science and Technology) Value distribution of some zeta functions
Odí Soler I Gibert (Autonomous University of Barcelona) Distortion and distribution of sets under inner functions
Elizabeth Strousse (Université Bordeaux 1) A variety of Szego-type results
Nicholas Young (Newcastle University & Leeds University) Duality methods for some two-point interpolation problems
El-Hassan Youssfi (Aix-Marseille Université) The polyanalytic reproducing kernels
Rachid Zarouf (Aix-Marseille Université) A duality approach to interpolation theory and application
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 ANR FRONT 2017
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