Pick Interpolation And Hilbert Function Spaces
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Pick Interpolation And Hilbert Function Spaces
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Author : Jim Agler
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-22
Pick Interpolation And Hilbert Function Spaces written by Jim Agler and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-22 with Mathematics categories.
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 Theory In Different Settings And Related Applications
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Author : Roland Duduchava
language : en
Publisher: Birkhäuser
Release Date : 2018-03-28
Operator Theory In Different Settings And Related Applications written by Roland Duduchava and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-28 with Mathematics categories.
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
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Author : Alberto A. Condori
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-30
Recent Progress In Function Theory And Operator Theory written by Alberto A. Condori and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-30 with Mathematics categories.
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.
The Corona Problem
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Author : Ronald G. Douglas
language : en
Publisher: Springer
Release Date : 2014-08-05
The Corona Problem written by Ronald G. Douglas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-05 with Mathematics categories.
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.
Catherine Beneteau Alberto A Condori Constanze Liaw William T Ross And Alan A Sola
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Author : Catherine Bénéteau:
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-12-22
Catherine Beneteau Alberto A Condori Constanze Liaw William T Ross And Alan A Sola written by Catherine Bénéteau: and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-22 with Mathematics categories.
This volume contains the Proceedings of the Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, held from June 29–July 3, 2015, at the Institut Mittag-Leffler, Djursholm, Sweden. The conference brought together experienced researchers and promising young mathematicians from many countries to discuss recent progress made in function theory, model spaces, completeness problems, and Carleson measures. This volume contains articles covering cutting-edge research questions, as well as longer survey papers and a report on the problem session that contains a collection of attractive open problems in complex and harmonic analysis.
Operator Theory Systems Theory And Scattering Theory Multidimensional Generalizations
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Author : Daniel Alpay
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Operator Theory Systems Theory And Scattering Theory Multidimensional Generalizations written by Daniel Alpay and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.
This volume contains a selection of papers, from experts in the area, on multidimensional operator theory. Topics considered include the non-commutative case, function theory in the polydisk, hyponormal operators, hyperanalytic functions, and holomorphic deformations of linear differential equations. Operator Theory, Systems Theory and Scattering Theory will be of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.
A First Course In Functional Analysis
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Author : Orr Moshe Shalit
language : en
Publisher: CRC Press
Release Date : 2017-03-16
A First Course In Functional Analysis written by Orr Moshe Shalit and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-16 with Mathematics categories.
Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside real applications in analysis. The background required for a student taking this course is minimal; basic linear algebra, calculus up to Riemann integration, and some acquaintance with topological and metric spaces.
Topics In Complex Analysis And Operator Theory
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Author : Oscar Blasco
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Topics In Complex Analysis And Operator Theory written by Oscar Blasco and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This book contains the lecture notes as well as some invited papers presented at the Third Winter School in Complex Analysis, Operator Theory and Applications held February 2-5, 2010, in Valencia, Spain. The book is divided into two parts. The first is an extended self-contained version of the mini-courses taught at the School. The papers in this first part are: Notes on real analytic functions and classical operators, by Pawel Domanski; Shining a Hilbertian lamp on the bidisk, by John E. McCarthy; Selected problems in perturbation theory, by Vladimir V. Peller; and Composition operators on Hardy-Orlicz spaces, by Luis Rodriguez-Piazza. The second part consists of several research papers on recent advances in the area and some survey articles of an expository character. The articles in this second part are: Remarks on weighted mixed norm spaces, by O. Blasco; Interpolation subspaces of $L^1$ of a vector measure and norm inequalities for the integration operator, by J.M. Calabuig, J. Rodriguez, and E.A. Sanchez-Perez; On the spectra of algebras of analytic functions, by D. Carando, D. Garcia, M. Maestre, and P. Sevilla-Peris; Holomorphic self-maps of the disk intertwining two linear fractional maps, by M.D. Contreras, S. Diaz-Madrigal, M.J. Martin, and D. Vukotic; ABC-type estimates via Garsia-type norms, by K.M. Dyakonov; and Volterra type operators on Bergman spaces with exponential weights, by J. Pau and J.A. Pelaez. The topics selected for the mini-courses cover several aspects of complex analysis and operator theory that play important roles in understanding connections between different areas that are considered in fashion these days. This part is aimed at graduate students and young researchers. The courses are self-contained, focusing on those aspects that are basic and that can lead the readers to a quick understanding of the theories presented in each topic. They start with the classical results and reach a selection of open problems in each case. The research and survey articles are aimed at young researchers in the area, as well as post-doc and senior researchers interested in complex analysis and operator theory. This book is published in cooperation with Real Sociedad Matematica Espanola.
Functional Analysis And Operator Algebras
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Author : Kenneth R. Davidson
language : en
Publisher: Springer Nature
Release Date : 2025-05-11
Functional Analysis And Operator Algebras written by Kenneth R. Davidson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-11 with Mathematics categories.
This book offers a comprehensive introduction to various aspects of functional analysis and operator algebras. In Part I, readers will find the foundational material suitable for a one-semester course on functional analysis and linear operators. Additionally, Part I includes enrichment topics that provide flexibility for instructors. Part II covers the fundamentals of Banach algebras and C*-algebras, followed by more advanced material on C* and von Neumann algebras. This section is suitable for use in graduate courses, with instructors having the option to select specific topics. Part III explores a range of important topics in operator theory and operator algebras. These include $H^p$ spaces, isometries and Toeplitz operators, nest algebras, dilation theory, applications to various classes of nonself-adjoint operator algebras, and noncommutative convexity and Choquet theory. This material is suitable for graduate courses and learning seminars, offering instructors flexibility in selecting topics.
Lectures On Analytic Function Spaces And Their Applications
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Author : Javad Mashreghi
language : en
Publisher: Springer Nature
Release Date : 2023-10-13
Lectures On Analytic Function Spaces And Their Applications written by Javad Mashreghi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-13 with Mathematics categories.
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.