Composition Operators On Spaces Of Analytic Functions
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Composition Operators On Spaces Of Analytic Functions
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Author : Carl C. Cowen Jr.
language : en
Publisher: Routledge
Release Date : 2019-03-04
Composition Operators On Spaces Of Analytic Functions written by Carl C. Cowen Jr. and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-04 with Mathematics categories.
The study of composition operators lies at the interface of analytic function theory and operator theory. Composition Operators on Spaces of Analytic Functions synthesizes the achievements of the past 25 years and brings into focus the broad outlines of the developing theory. It provides a comprehensive introduction to the linear operators of composition with a fixed function acting on a space of analytic functions. This new book both highlights the unifying ideas behind the major theorems and contrasts the differences between results for related spaces. Nine chapters introduce the main analytic techniques needed, Carleson measure and other integral estimates, linear fractional models, and kernel function techniques, and demonstrate their application to problems of boundedness, compactness, spectra, normality, and so on, of composition operators. Intended as a graduate-level textbook, the prerequisites are minimal. Numerous exercises illustrate and extend the theory. For students and non-students alike, the exercises are an integral part of the book. By including the theory for both one and several variables, historical notes, and a comprehensive bibliography, the book leaves the reader well grounded for future research on composition operators and related areas in operator or function theory.
Composition Operators And Classical Function Theory
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Author : Joel H. Shapiro
language : en
Publisher:
Release Date : 1993
Composition Operators And Classical Function Theory written by Joel H. Shapiro and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The study of composition operators forges links between fundamental properties of linear operators and beautiful results from the classical theory of analytic functions. This book provides a self-contained introduction to both the subject and its function-theoretic underpinnings. The development is geometrically motivated, and accessible to anyone who has studied basic graduate-level real and complex analysis. The work explores how operator-theoretic issues such as boundedness, compactness, and cyclicity evolve - in the setting of composition operators on the Hilbert space H2 into questions about subordination, value distribution, angular derivatives, iteration, and functional equations. Each of these classical topics is developed fully, and particular attention is paid to their common geometric heritage as descendants of the Schwarz Lemma.
Banach Spaces Of Analytic Functions
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Author : Thomas H. MacGregor
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Banach Spaces Of Analytic Functions written by Thomas H. MacGregor 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 2008 with Mathematics categories.
This volume is focused on Banach spaces of functions analytic in the open unit disc, such as the classical Hardy and Bergman spaces, and weighted versions of these spaces. Other spaces under consideration here include the Bloch space, the families of Cauchy transforms and fractional Cauchy transforms, BMO, VMO, and the Fock space. Some of the work deals with questions about functions in several complex variables.
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.
Operator Theory In Function Spaces
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Author : Kehe Zhu
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Operator Theory In Function Spaces written by Kehe Zhu 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 2007 with Mathematics categories.
This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.
Handbook Of Analytic Operator Theory
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Author : Kehe Zhu
language : en
Publisher: CRC Press
Release Date : 2019-05-10
Handbook Of Analytic Operator Theory written by Kehe Zhu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-10 with Mathematics categories.
This handbook concerns the subject of holomorphic function spaces and operators acting on them. Topics include Bergman spaces, Hardy spaces, Besov/Sobolev spaces, Fock spaces, and the space of Dirichlet series. Operators discussed in the book include Toeplitz operators, Hankel operators, composition operators, and Cowen-Douglas class operators
Dynamics Of Linear Operators
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Author : Frédéric Bayart
language : en
Publisher: Cambridge University Press
Release Date : 2009-06-04
Dynamics Of Linear Operators written by Frédéric Bayart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-04 with Mathematics categories.
The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators. Written for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.
Function Theory And P Spaces
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Author : Raymond Cheng
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-28
Function Theory And P Spaces written by Raymond Cheng 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 2020-05-28 with Education categories.
The classical ℓp sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces ℓpA of analytic functions whose Taylor coefficients belong to ℓp. Relations between the Banach space ℓp and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of ℓpA and a discussion of the Wiener algebra ℓ1A. Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.
Absolutely Summing Operators
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Author : Joe Diestel
language : en
Publisher: Cambridge University Press
Release Date : 1995-04-27
Absolutely Summing Operators written by Joe Diestel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-27 with Mathematics categories.
This text provides the beginning graduate student with an account of p-summing and related operators.
Hilbert Spaces Of Analytic Functions
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Author : Javad Mashreghi
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-01-01
Hilbert Spaces Of Analytic Functions written by Javad Mashreghi 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 2010-01-01 with Mathematics categories.