Universitext: Tracts in Mathematics

Composition Operators

and Classical Function Theory

Authors: Shapiro, Joel H.

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About this Textbook

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.

Table of contents (11 chapters)

Buy this book

eBook $49.99
price for USA (gross)
  • ISBN 978-1-4612-0887-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $64.95
price for USA
  • ISBN 978-0-387-94067-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Composition Operators
Book Subtitle
and Classical Function Theory
Authors
Series Title
Universitext: Tracts in Mathematics
Copyright
1993
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0887-7
DOI
10.1007/978-1-4612-0887-7
Softcover ISBN
978-0-387-94067-0
Edition Number
1
Number of Pages
XVI, 223
Number of Illustrations and Tables
6 b/w illustrations
Topics