Composition Operators And Classical Function Theory
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Composition Operators
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Author : Joel H. Shapiro
language : en
Publisher: Springer
Release Date : 1993-08-26
Composition Operators written by Joel H. Shapiro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-08-26 with Mathematics categories.
The study of composition operators links some of the most basic questions you can ask about linear operators with beautiful classical results from analytic-function theory. The process invests old theorems with new mean ings, and bestows upon functional analysis an intriguing class of concrete linear operators. Best of all, the subject can be appreciated by anyone with an interest in function theory or functional analysis, and a background roughly equivalent to the following twelve chapters of Rudin's textbook Real and Complex Analysis [Rdn '87]: Chapters 1-7 (measure and integra tion, LP spaces, basic Hilbert and Banach space theory), and 10-14 (basic function theory through the Riemann Mapping Theorem). In this book I introduce the reader to both the theory of composition operators, and the classical results that form its infrastructure. I develop the subject in a way that emphasizes its geometric content, staying as much as possible within the prerequisites set out in the twelve fundamental chapters of Rudin's book. Although much of the material on operators is quite recent, this book is not intended to be an exhaustive survey. It is, quite simply, an invitation to join in the fun. The story goes something like this.
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.
Algorithmic Number Theory
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Author : Joe P. Buhler
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-06-05
Algorithmic Number Theory written by Joe P. Buhler 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 1998-06-05 with Computers categories.
The field of diagnostic nuclear medicine has changed significantly during the past decade. This volume is designed to present the student and the professional with a comprehensive update of recent developments not found in other textbooks on the subject. The various clinical applications of nuclear medicine techniques are extensively considered, and due attention is given also to radiopharmaceuticals, equipment and instrumentation, reconstruction techniques and the principles of gene imaging.
Constructive Experimental And Nonlinear Analysis
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Author : Michel A. Théra
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Constructive Experimental And Nonlinear Analysis written by Michel A. Théra 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 2000 with Mathematics categories.
Presents 20 papers on different aspects of modern analysis including analytic and computational number theory, symbolic and numerical computation, theoretical and computational optimization, and recent development in non-smooth and functional analysis with applications to control theory. Applications in algorithmic number theory and tomography are also discussed. Many of the papers originated at a September 1999 workshop held at the University of Limoges. Among the topics are vector-valued perturbed minimization principles; rotundity related to Lipschitz separation; continued fractions, comparison algorithms, and fine structure constants; and codirectional compactness, metric regularity, and subdifferential calculus. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Composition Operators On Spaces Of Analytic Functions
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Author : Carl C. Cowen, Jr.
language : en
Publisher: CRC Press
Release Date : 1995-04-27
Composition Operators On Spaces Of Analytic Functions written by Carl C. Cowen, Jr. and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-27 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.
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.
Recent Advances In Operator Related Function Theory
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Author : Alec L. Matheson
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Recent Advances In Operator Related Function Theory written by Alec L. Matheson 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 2006 with Mathematics categories.
The articles in this book are based on talks at a conference devoted to interrelations between function theory and the theory of operators. The main theme of the book is the role of Alexandrov-Clark measures. Two of the articles provide the introduction to the theory of Alexandrov-Clark measures and to its applications in the spectral theory of linear operators. The remaining articles deal with recent results in specific directions related to the theme of the book.
Functional Analysis With Current Applications In Science Technology And Industry
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Author : Martin Brokate
language : en
Publisher: CRC Press
Release Date : 2021-02-27
Functional Analysis With Current Applications In Science Technology And Industry written by Martin Brokate and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-27 with Mathematics categories.
This volume constitutes the proceedings of a conference on functional analysis and its applications, which took place in India during December 1996. Topics include topological vector spaces, Banach algebras, meromorphic functions, partial differential equations, variational equations and inequalities, optimization, wavelets, elastroplasticity, numerical integration, fractal image compression, reservoir simulation, forest management, and industrial maths.
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.
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.