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Composition Operators

and Classical Function Theory

  • Joel H. Shapiro

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

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Joel H. Shapiro
    Pages 1-8
  3. Joel H. Shapiro
    Pages 9-20
  4. Joel H. Shapiro
    Pages 21-35
  5. Joel H. Shapiro
    Pages 37-53
  6. Joel H. Shapiro
    Pages 55-76
  7. Joel H. Shapiro
    Pages 77-87
  8. Joel H. Shapiro
    Pages 89-105
  9. Joel H. Shapiro
    Pages 107-128
  10. Joel H. Shapiro
    Pages 129-145
  11. Joel H. Shapiro
    Pages 147-175
  12. Joel H. Shapiro
    Pages 177-197
  13. Back Matter
    Pages 199-224

About this book

Introduction

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.

Keywords

Complex analysis Derivative Hilbert space Schwarz lemma compactness differential equation

Authors and affiliations

  • Joel H. Shapiro
    • 1
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0887-7
  • Copyright Information Springer-Verlag New York, Inc. 1993
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94067-0
  • Online ISBN 978-1-4612-0887-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site