Composition Operators

and Classical Function Theory

By: Joel H. Shapiro

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Paperback | 16 September 1993

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244 Pages

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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.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Complex Analysis

Preface
Acknowledgments
Notation and Terminology
Linear Fractional Prologue	p. 1
Littlewood's Theorem	p. 9
Compactness: Introduction	p. 21
Compactness and Univalence	p. 37
The Angular Derivative	p. 55
Angular Derivatives and Iteration	p. 77
Compactness and Eigenfunctions	p. 89
Linear Fractional Cyclicity	p. 107
Cyclicity and Models	p. 129
Compactness from Models	p. 147
Compactness: General Case	p. 177
Epilogue	p. 199
References	p. 203
Symbol Index	p. 215
Author Index	p. 217
Subject Index	p. 220
Table of Contents provided by Blackwell. All Rights Reserved.

Composition Operators

and Classical Function Theory

At a Glance

Paperback

Shipping

How to return your order

Defective items

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