Studies on Composition Operators
Studies on Composition Operators

Author: Rocky Mountain Mathematics Consortium

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 266

ISBN-13: 0821807684

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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
Composition Operators on Spaces of Analytic Functions

Author: Carl C. Cowen Jr.

Publisher: Routledge

Published: 2019-03-04

Total Pages: 404

ISBN-13: 1351459139

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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 on Function Spaces
Composition Operators on Function Spaces

Author: R.K. Singh

Publisher: Elsevier

Published: 1993-11-03

Total Pages: 327

ISBN-13: 0080872905

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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.

Composition Operators
Composition Operators

Author: Joel H. Shapiro

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 229

ISBN-13: 1461208874

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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.

Analysis of Toeplitz Operators
Analysis of Toeplitz Operators

Author: Albrecht Böttcher

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 511

ISBN-13: 366202652X

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A revised introduction to the advanced analysis of block Toeplitz operators including recent research. This book builds on the success of the first edition which has been used as a standard reference for fifteen years. Topics range from the analysis of locally sectorial matrix functions to Toeplitz and Wiener-Hopf determinants. This will appeal to both graduate students and specialists in the theory of Toeplitz operators.

Dynamics of Linear Operators
Dynamics of Linear Operators

Author: Frédéric Bayart

Publisher: Cambridge University Press

Published: 2009-06-04

Total Pages: 352

ISBN-13: 0521514967

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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.

Absolutely Summing Operators
Absolutely Summing Operators

Author: Joe Diestel

Publisher: Cambridge University Press

Published: 1995-04-27

Total Pages: 494

ISBN-13: 9780521431682

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This text provides the beginning graduate student with an account of p-summing and related operators.

Nonlinear Superposition Operators
Nonlinear Superposition Operators

Author: Jurgen Appell

Publisher: Cambridge University Press

Published: 1990

Total Pages: 0

ISBN-13: 0521361028

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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 Classes on the Unit Disc
Function Classes on the Unit Disc

Author: Miroslav Pavlović

Publisher: Walter de Gruyter

Published: 2013-12-12

Total Pages: 463

ISBN-13: 3110281902

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This monograph contains a study on various function classes, a number of new results and new or easy proofs of old results (Fefferman-Stein theorem on subharmonic behavior, theorems on conjugate functions and fractional integration on Bergman spaces, Fefferman's duality theorem), which are interesting for specialists; applications of the Hardy-Littlewood inequalities on Taylor coefficients to (C, α)-maximal theorems and (C, α)-convergence; a study of BMOA, due to Knese, based only on Green's formula; the problem of membership of singular inner functions in Besov and Hardy-Sobolev spaces; a full discussion of g-function (all p > 0) and Calderón's area theorem; a new proof, due to Astala and Koskela, of the Littlewood-Paley inequality for univalent functions; and new results and proofs on Lipschitz spaces, coefficient multipliers and duality, including compact multipliers and multipliers on spaces with non-normal weights. It also contains a discussion of analytic functions and lacunary series with values in quasi-Banach spaces with applications to function spaces and composition operators. Sixteen open questions are posed. The reader is assumed to have a good foundation in Lebesgue integration, complex analysis, functional analysis, and Fourier series. Further information can be found at the author's website at http://poincare.matf.bg.ac.rs/~pavlovic.

Function Theory in the Unit Ball of Cn
Function Theory in the Unit Ball of Cn

Author: W. Rudin

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 449

ISBN-13: 1461380987

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Around 1970, an abrupt change occurred in the study of holomorphic functions of several complex variables. Sheaves vanished into the back ground, and attention was focused on integral formulas and on the "hard analysis" problems that could be attacked with them: boundary behavior, complex-tangential phenomena, solutions of the J-problem with control over growth and smoothness, quantitative theorems about zero-varieties, and so on. The present book describes some of these developments in the simple setting of the unit ball of en. There are several reasons for choosing the ball for our principal stage. The ball is the prototype of two important classes of regions that have been studied in depth, namely the strictly pseudoconvex domains and the bounded symmetric ones. The presence of the second structure (i.e., the existence of a transitive group of automorphisms) makes it possible to develop the basic machinery with a minimum of fuss and bother. The principal ideas can be presented quite concretely and explicitly in the ball, and one can quickly arrive at specific theorems of obvious interest. Once one has seen these in this simple context, it should be much easier to learn the more complicated machinery (developed largely by Henkin and his co-workers) that extends them to arbitrary strictly pseudoconvex domains. In some parts of the book (for instance, in Chapters 14-16) it would, however, have been unnatural to confine our attention exclusively to the ball, and no significant simplifications would have resulted from such a restriction.