Composition Operators on Spaces of Analytic Functions

✍ Scribed by Carl C. Cowen Jr., Barbara I. MacCluer

• Publisher: CRC Press
• Year: 1995
• Tongue: English
• Leaves: 407
• Series: Studies in Advanced Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Content: Introduction Analysis Background A Menagerie of Spaces Some Theorems on Integration Geometric Function Theory in the Disk Iteration of Functions in the Disk The Automorphisms of the Ball Julia-Caratheodory Theory in the Ball Norms Boundedness in Classical Spaces on the Disk Compactness and Essential Norms in Classical Spaces on the Disk Hilbert-Schmidt Operators Composition Operators with Closed Range Boundedness on Hp (BN) Small Spaces Compactness on Small Spaces Boundedness on Small Spaces Large Spaces Boundedness on Large Spaces Compactness on Large Spaces Hilbert-Schmidt Operators Special Results for Several Variables Compactness Revisited Wogen's Theorem Spectral Properties Introduction Invertible Operators on the Classical Spaces on the Disk Invertible Operators on the Classical Spaces on the Ball Spectra of Compact Composition Operators Spectra: Boundary Fixed Point, j'(a)

✦ Subjects

Funzioni analitiche;Operatori lineari