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Studies On Composition Operators And Function Spaces

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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.

Studies On Composition Operators And Function Spaces

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Author : Marko Kotilainen
language : en
Publisher:
Release Date : 2007

Studies On Composition Operators And Function Spaces written by Marko Kotilainen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Composition operators categories.

This survey part of the thesis contains some background to the series of studies on composition operators and function spaces. Bounded and compact composition operators are studied in analytic Qk type spaces and in some real function spaces. So-called Bloch-Sobolev spaces are introduced. An asymptotic formula for the essential norm of the composition operator mapping into Qk(p,q) is established. Carleson measures are studied in higher dimensions and used in the study of hyperbolic harmonic function spaces. A short summary of the articles is included.

Composition Operators On Function Spaces

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Author : R.K. Singh
language : en
Publisher: Elsevier
Release Date : 1993-11-03

Composition Operators On Function Spaces written by R.K. Singh and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-11-03 with Mathematics categories.

This volume of the Mathematics Studies presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mathematical physics.After an introduction, the book deals with these operators on Lp-spaces. This study is useful in measurable dynamics, ergodic theory, classical mechanics and Markov process. The composition operators on functional Banach spaces (including Hardy spaces) are studied in chapter III. This chapter makes contact with the theory of analytic functions of complex variables. Chapter IV presents a study of these operators on locally convex spaces of continuous functions making contact with topological dynamics. In the last chapter of the book some applications of composition operators in isometries, ergodic theory and dynamical systems are presented. An interesting interplay of algebra, topology, and analysis is displayed.This comprehensive and up-to-date study of composition operators on different function spaces should appeal to research workers in functional analysis and operator theory, post-graduate students of mathematics and statistics, as well as to physicists and engineers.

Studies On Composition Operators

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Author : Rocky Mountain Mathematics Consortium
language : en
Publisher: American Mathematical Soc.
Release Date : 1998

Studies On Composition Operators written by Rocky Mountain Mathematics Consortium 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 1998 with Mathematics categories.

This book reflects the proceedings of the 1996 Rocky Mountain Mathematics Consortium conference on "Composition Operators on Spaces of Analytic Functions" held at the University of Wyoming. The readers will find here a collection of high-quality research and expository articles on composition operators in one and several variables. The book highlights open questions and new advances in the classical areas and promotes topics which are left largely untreated in the existing texts. In the past two decades, the study of composition operators has experienced tremendous growth. Many connections between the study of these operators on various function spaces and other branches of analysis have been established. Advances in establishing criteria for membership in different operator classes have led to progress in the study of the spectra, adjoints, and iterates of these operators. More recently, connections between these operators and the study of the invariant subspace problem, functional equations, and dynamical systems have been exploited.

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.

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.

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

Nonlinear Superposition Operators

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Author : Jurgen Appell
language : en
Publisher: Cambridge University Press
Release Date : 1990

Nonlinear Superposition Operators written by Jurgen Appell 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 1990 with Mathematics categories.

Aiming to present a self-contained account of the present state of knowledge of the theory of the non-linear superposition operators - a generalization of the notion of functions - this book diverges from classical nonlinear analysis and is applicable to operators in a variety of function spaces.

Function Spaces In Analysis

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Author : Krzysztof Jarosz
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-07-28

Function Spaces In Analysis written by Krzysztof Jarosz 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 2015-07-28 with Education categories.

This volume contains the proceedings of the Seventh Conference on Function Spaces, which was held from May 20-24, 2014 at Southern Illinois University at Edwardsville. 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), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.

Classical Descriptive Set Theory

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Author : Alexander Kechris
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Classical Descriptive Set Theory written by Alexander Kechris 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 2012-12-06 with Mathematics categories.

Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation.

Studies On Composition Operators And Function Spaces

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