Pick Interpolation And Hilbert Function Spaces

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Pick Interpolation and Hilbert Function Spaces

Jim Agler,John E. McCarthy
Pick Interpolation and Hilbert Function Spaces Book PDF

Author : Jim Agler,John E. McCarthy
Publisher : American Mathematical Society
Page : 330 pages
File Size : 42,9 Mb
Release : 2023-02-22
Category : Mathematics
ISBN : 9781470468552

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Pick Interpolation and Hilbert Function Spaces by Jim Agler,John E. McCarthy Pdf

The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.

Operator Analysis

Jim Agler,John Edward McCarthy,Nicholas John Young
Operator Analysis Book PDF

Author : Jim Agler,John Edward McCarthy,Nicholas John Young
Publisher : Cambridge University Press
Page : 393 pages
File Size : 45,6 Mb
Release : 2020-03-26
Category : Mathematics
ISBN : 9781108485449

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Operator Analysis by Jim Agler,John Edward McCarthy,Nicholas John Young Pdf

This monograph, aimed at graduate students and researchers, explores the use of Hilbert space methods in function theory. Explaining how operator theory interacts with function theory in one and several variables, the authors journey from an accessible explanation of the techniques to their uses in cutting edge research.

Function Spaces

Conference on Function Spaces
Function Spaces Book PDF

Author : Conference on Function Spaces
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 54,7 Mb
Release : 2007
Category : Function spaces
ISBN : 9780821840610

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Function Spaces by Conference on Function Spaces Pdf

This book consists of contributions by the participants of the Fifth Conference on Function Spaces, held at Southern Illinois University in May of 2006. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $L{p $-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. The goal of the conference was to bring together mathematicians interested in various problems related to function spaces and to facilitate the exchange of ideas between people working on similar problems. Hence, the majority of papers in this book are accessible to non-experts. Some articles contain expositions of known results and discuss open problems, others contain new results.

The Dirichlet Space and Related Function Spaces

Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer,Brett D. Wick
The Dirichlet Space and Related Function Spaces Book PDF

Author : Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer,Brett D. Wick
Publisher : American Mathematical Soc.
Page : 536 pages
File Size : 40,5 Mb
Release : 2019-09-03
Category : Dirichlet principle
ISBN : 9781470450823

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The Dirichlet Space and Related Function Spaces by Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer,Brett D. Wick Pdf

The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.

Analysis of Operators on Function Spaces

Alexandru Aleman,Haakan Hedenmalm,Dmitry Khavinson,Mihai Putinar
Analysis of Operators on Function Spaces Book PDF

Author : Alexandru Aleman,Haakan Hedenmalm,Dmitry Khavinson,Mihai Putinar
Publisher : Springer
Page : 281 pages
File Size : 43,5 Mb
Release : 2019-05-30
Category : Mathematics
ISBN : 9783030146405

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Analysis of Operators on Function Spaces by Alexandru Aleman,Haakan Hedenmalm,Dmitry Khavinson,Mihai Putinar Pdf

This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.

Interpolation and Sampling in Spaces of Analytic Functions

Kristian Seip
Interpolation and Sampling in Spaces of Analytic Functions Book PDF

Author : Kristian Seip
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 41,5 Mb
Release : 2004
Category : Analytic functions
ISBN : 9780821835548

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Interpolation and Sampling in Spaces of Analytic Functions by Kristian Seip Pdf

Based on a series of six lectures given by the author at the University of Michigan, this book is intended as an introduction to the topic of interpolation and sampling in analytic function spaces. The three major topics covered are Nevanlinna-Pick interpolation, Carleson's interpolation theorem, an

Function Spaces, Theory and Applications

Ilia Binder,Damir Kinzebulatov,Javad Mashreghi
Function Spaces Theory and Applications Book PDF

Author : Ilia Binder,Damir Kinzebulatov,Javad Mashreghi
Publisher : Springer Nature
Page : 487 pages
File Size : 54,9 Mb
Release : 2024-01-12
Category : Mathematics
ISBN : 9783031392702

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Function Spaces, Theory and Applications by Ilia Binder,Damir Kinzebulatov,Javad Mashreghi Pdf

The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They also have several essential applications in other fields of mathematics and engineering, e.g., robust control engineering, signal and image processing, and theory of communication. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins, e.g. the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b), have also been the center of attention in the past two decades. Studying the Hilbert spaces of analytic functions and the operators acting on them, as well as their applications in other parts of mathematics or engineering were the main subjects of this program. During the program, the world leading experts on function spaces gathered and discussed the new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With more than 250 hours of lectures by prominent mathematicians, a wide variety of topics were covered. More explicitly, there were mini-courses and workshops on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Blaschke Products and Inner Functions, Discrete and Continuous Semigroups of Composition Operators, The Corona Problem, Non-commutative Function Theory, Drury-Arveson Space, and Convergence of Scattering Data and Non-linear Fourier Transform. At the end of each week, there was a high profile colloquium talk on the current topic. The program also contained two semester-long advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. The current volume features a more detailed version of some of the talks presented during the program.

A Glimpse at Hilbert Space Operators

Sheldon Axler,Peter Rosenthal,Donald Sarason
A Glimpse at Hilbert Space Operators Book PDF

Author : Sheldon Axler,Peter Rosenthal,Donald Sarason
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 40,6 Mb
Release : 2011-04-13
Category : Mathematics
ISBN : 9783034603478

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A Glimpse at Hilbert Space Operators by Sheldon Axler,Peter Rosenthal,Donald Sarason Pdf

Paul Richard Halmos, who lived a life of unbounded devotion to mathematics and to the mathematical community, died at the age of 90 on October 2, 2006. This volume is a memorial to Paul by operator theorists he inspired. Paul’sinitial research,beginning with his 1938Ph.D. thesis at the University of Illinois under Joseph Doob, was in probability, ergodic theory, and measure theory. A shift occurred in the 1950s when Paul’s interest in foundations led him to invent a subject he termed algebraic logic, resulting in a succession of papers on that subject appearing between 1954 and 1961, and the book Algebraic Logic, published in 1962. Paul’s ?rst two papers in pure operator theory appeared in 1950. After 1960 Paul’s research focused on Hilbert space operators, a subject he viewed as enc- passing ?nite-dimensional linear algebra. Beyond his research, Paul contributed to mathematics and to its community in manifold ways: as a renowned expositor, as an innovative teacher, as a tireless editor, and through unstinting service to the American Mathematical Society and to the Mathematical Association of America. Much of Paul’s in?uence ?owed at a personal level. Paul had a genuine, uncalculating interest in people; he developed an enormous number of friendships over the years, both with mathematicians and with nonmathematicians. Many of his mathematical friends, including the editors ofthisvolume,whileabsorbingabundantquantitiesofmathematicsatPaul’sknee, learned from his advice and his example what it means to be a mathematician.

Interpolation and Realization Theory with Applications to Control Theory

Vladimir Bolotnikov,Sanne ter Horst,André C.M. Ran,Victor Vinnikov
Interpolation and Realization Theory with Applications to Control Theory Book PDF

Author : Vladimir Bolotnikov,Sanne ter Horst,André C.M. Ran,Victor Vinnikov
Publisher : Springer
Page : 353 pages
File Size : 48,6 Mb
Release : 2019-04-08
Category : Mathematics
ISBN : 9783030116149

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Interpolation and Realization Theory with Applications to Control Theory by Vladimir Bolotnikov,Sanne ter Horst,André C.M. Ran,Victor Vinnikov Pdf

This volume is devoted to Joseph A. (Joe) Ball’s contributions to operator theory and its applications and in celebration of his seventieth birthday. Joe Ball’s career spans over four and a half decades, starting with his work on model theory and related topics for non-contractions and operators on multiply connected domains. Later on, more applied operator theory themes appeared in his work, involving factorization and interpolation for operator-valued functions, with extensive applications in system and control theory. He has worked on nonlinear control, time-varying systems and, more recently, on multidimensional systems and noncommutative H∞-theory on the unit ball and polydisk, and more general domains, and these are only the main themes in his vast oeuvre. Fourteen research papers constitute the core of this volume, written by mathematicians who have collaborated with Joe or have been influenced by his vast mathematical work. A curriculum vitae, a publications list and a list of Joe Ball’s PhD students are included in this volume, as well as personal reminiscences by colleagues and friends. Contributions by Yu. M. Arlinskii, S. Hassi, M. Augat, J. W. Helton, I. Klep, S. McCullough, S. Balasubramanian, U. Wijesooriya, N. Cohen, Q. Fang, S. Gorai, J. Sarkar, G. J. Groenewald, S. ter Horst, J. Jaftha, A. C. M. Ran, M.A. Kaashoek, F. van Schagen, A. Kheifets, Z. A. Lykova, N. J. Young, A. E. Ajibo, R. T. W. Martin, A. Ramanantoanina, M.-J. Y. Ou, H. J. Woerdeman, A. van der Schaft, A. Tannenbaum, T. T. Georgiou, J. O. Deasy and L. Norton.

Lectures on Analytic Function Spaces and their Applications

Javad Mashreghi
Lectures on Analytic Function Spaces and their Applications Book PDF

Author : Javad Mashreghi
Publisher : Springer Nature
Page : 426 pages
File Size : 44,8 Mb
Release : 2023-11-14
Category : Mathematics
ISBN : 9783031335723

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Lectures on Analytic Function Spaces and their Applications by Javad Mashreghi Pdf

The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They have essential applications in other fields of mathematics and engineering. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins—the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b)—have also garnered attention in recent decades. Leading experts on function spaces gathered and discussed new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With over 250 hours of lectures by prominent mathematicians, the program spanned a wide variety of topics. More explicitly, there were courses and workshops on Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Blaschke Products and Inner Functions, and Convergence of Scattering Data and Non-linear Fourier Transform, among others. At the end of each week, there was a high-profile colloquium talk on the current topic. The program also contained two advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. This volume features the courses given on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Semigroups of weighted composition operators on spaces of holomorphic functions, the Corona Problem, Non-commutative Function Theory, and Drury-Arveson Space. This volume is a valuable resource for researchers interested in analytic function spaces.

Functional Analysis, Harmonic Analysis, and Image Processing: A Collection of Papers in Honor of Björn Jawerth

Michael Cwikel,Mario Milman
Functional Analysis Harmonic Analysis and Image Processing A Collection of Papers in Honor of Bj rn Jawerth Book PDF

Author : Michael Cwikel,Mario Milman
Publisher : American Mathematical Soc.
Page : 411 pages
File Size : 53,6 Mb
Release : 2017-07-26
Category : Fourier analysis
ISBN : 9781470428365

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Functional Analysis, Harmonic Analysis, and Image Processing: A Collection of Papers in Honor of Björn Jawerth by Michael Cwikel,Mario Milman Pdf

This volume is dedicated to the memory of Björn Jawerth. It contains original research contributions and surveys in several of the areas of mathematics to which Björn made important contributions. Those areas include harmonic analysis, image processing, and functional analysis, which are of course interrelated in many significant and productive ways. Among the contributors are some of the world's leading experts in these areas. With its combination of research papers and surveys, this book may become an important reference and research tool. This book should be of interest to advanced graduate students and professional researchers in the areas of functional analysis, harmonic analysis, image processing, and approximation theory. It combines articles presenting new research with insightful surveys written by foremost experts.

Operator Theory, Function Spaces, and Applications

Tanja Eisner,Birgit Jacob,André Ran,Hans Zwart
Operator Theory Function Spaces and Applications Book PDF

Author : Tanja Eisner,Birgit Jacob,André Ran,Hans Zwart
Publisher : Birkhäuser
Page : 233 pages
File Size : 51,8 Mb
Release : 2016-09-24
Category : Mathematics
ISBN : 9783319313832

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Operator Theory, Function Spaces, and Applications by Tanja Eisner,Birgit Jacob,André Ran,Hans Zwart Pdf

This volume collects a selected number of papers presented at the International Workshop on Operator Theory and its Applications (IWOTA) held in July 2014 at Vrije Universiteit in Amsterdam. Main developments in the broad area of operator theory are covered, with special emphasis on applications to science and engineering. The volume also presents papers dedicated to the eightieth birthday of Damir Arov and to the sixty-fifth birthday of Leiba Rodman, both leading figures in the area of operator theory and its applications, in particular, to systems theory.

The Corona Problem

Ronald G. Douglas,Steven G. Krantz,Eric T. Sawyer,Sergei Treil,Brett D. Wick
The Corona Problem Book PDF

Author : Ronald G. Douglas,Steven G. Krantz,Eric T. Sawyer,Sergei Treil,Brett D. Wick
Publisher : Springer
Page : 231 pages
File Size : 50,6 Mb
Release : 2014-08-05
Category : Mathematics
ISBN : 9781493912551

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The Corona Problem by Ronald G. Douglas,Steven G. Krantz,Eric T. Sawyer,Sergei Treil,Brett D. Wick Pdf

The purpose of the corona workshop was to consider the corona problem in both one and several complex variables, both in the context of function theory and harmonic analysis as well as the context of operator theory and functional analysis. It was held in June 2012 at the Fields Institute in Toronto, and attended by about fifty mathematicians. This volume validates and commemorates the workshop, and records some of the ideas that were developed within. The corona problem dates back to 1941. It has exerted a powerful influence over mathematical analysis for nearly 75 years. There is material to help bring people up to speed in the latest ideas of the subject, as well as historical material to provide background. Particularly noteworthy is a history of the corona problem, authored by the five organizers, that provides a unique glimpse at how the problem and its many different solutions have developed. There has never been a meeting of this kind, and there has never been a volume of this kind. Mathematicians—both veterans and newcomers—will benefit from reading this book. This volume makes a unique contribution to the analysis literature and will be a valuable part of the canon for many years to come.

Operator Theory in Different Settings and Related Applications

Roland Duduchava,Marinus A. Kaashoek,Nikolai Vasilevski,Victor Vinnikov
Operator Theory in Different Settings and Related Applications Book PDF

Author : Roland Duduchava,Marinus A. Kaashoek,Nikolai Vasilevski,Victor Vinnikov
Publisher : Birkhäuser
Page : 309 pages
File Size : 45,7 Mb
Release : 2018-03-28
Category : Mathematics
ISBN : 9783319625270

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Operator Theory in Different Settings and Related Applications by Roland Duduchava,Marinus A. Kaashoek,Nikolai Vasilevski,Victor Vinnikov Pdf

This book provides a selection of reports and survey articles on the latest research in the area of single and multivariable operator theory and related fields. The latter include singular integral equations, ordinary and partial differential equations, complex analysis, numerical linear algebra, and real algebraic geometry – all of which were among the topics presented at the 26th International Workshop in Operator Theory and its Applications, held in Tbilisi, Georgia, in the summer of 2015. Moreover, the volume includes three special commemorative articles. One of them is dedicated to the memory of Leiba Rodman, another to Murray Marshall, and a third to Boris Khvedelidze, an outstanding Georgian mathematician and one of the founding fathers of the theory of singular integral equations. The book will be of interest to a broad range of mathematicians, from graduate students to researchers, whose primary interests lie in operator theory, complex analysis and applications, as well as specialists in mathematical physics.

Recent Progress in Function Theory and Operator Theory

Alberto A. Condori,Elodie Pozzi,William T. Ross,Alan A. Sola
Recent Progress in Function Theory and Operator Theory Book PDF

Author : Alberto A. Condori,Elodie Pozzi,William T. Ross,Alan A. Sola
Publisher : American Mathematical Society
Page : 226 pages
File Size : 48,5 Mb
Release : 2024-04-30
Category : Mathematics
ISBN : 9781470472467

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Recent Progress in Function Theory and Operator Theory by Alberto A. Condori,Elodie Pozzi,William T. Ross,Alan A. Sola Pdf

This volume contains the proceedings of the AMS Special Session on Recent Progress in Function Theory and Operator Theory, held virtually on April 6, 2022. Function theory is a classical subject that examines the properties of individual elements in a function space, while operator theory usually deals with concrete operators acting on such spaces or other structured collections of functions. These topics occupy a central position in analysis, with important connections to partial differential equations, spectral theory, approximation theory, and several complex variables. With the aid of certain canonical representations or “models”, the study of general operators can often be reduced to that of the operator of multiplication by one or several independent variables, acting on spaces of analytic functions or compressions of this operator to co-invariant subspaces. In this way, a detailed understanding of operators becomes connected with natural questions concerning analytic functions, such as zero sets, constructions of functions constrained by norms or interpolation, multiplicative structures granted by factorizations in spaces of analytic functions, and so forth. In many cases, non-obvious problems initially motivated by operator-theoretic considerations turn out to be interesting on their own, leading to unexpected challenges in function theory. The research papers in this volume deal with the interplay between function theory and operator theory and the way in which they influence each other.