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Composition Operators

and Classical Function Theory

  • Textbook
  • © 1993

Overview

Authors:
  1. Joel H. Shapiro

    1. Department of Mathematics, Michigan State University, East Lansing, USA

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Part of the book series: Universitext (UTX)

Part of the book sub series: Universitext: Tracts in Mathematics (3080)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Linear Fractional Prologue

    • Joel H. Shapiro
    Pages 1-8

  3. Littlewood’s Theorem

    • Joel H. Shapiro
    Pages 9-20

  4. Compactness: Introduction

    • Joel H. Shapiro
    Pages 21-35

  5. Compactness and Univalence

    • Joel H. Shapiro
    Pages 37-53

  6. The Angular Derivative

    • Joel H. Shapiro
    Pages 55-76

  7. Angular Derivatives and Iteration

    • Joel H. Shapiro
    Pages 77-87

  8. Compactness and Eigenfunctions

    • Joel H. Shapiro
    Pages 89-105

  9. Linear Fractional Cyclicity

    • Joel H. Shapiro
    Pages 107-128

  10. Cyclicity and Models

    • Joel H. Shapiro
    Pages 129-145

  11. Compactness from Models

    • Joel H. Shapiro
    Pages 147-175

  12. Compactness: General Case

    • Joel H. Shapiro
    Pages 177-197

  13. Back Matter

    Pages 199-224
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Michigan State University, East Lansing, USA

    Joel H. Shapiro

Bibliographic Information

  • Book Title: Composition Operators

  • Book Subtitle: and Classical Function Theory

  • Authors: Joel H. Shapiro

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4612-0887-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1993

  • Softcover ISBN: 978-0-387-94067-0Published: 26 August 1993

  • eBook ISBN: 978-1-4612-0887-7Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XVI, 223

  • Number of Illustrations: 6 b/w illustrations

  • Topics: Analysis

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