Cyclic phenomena for composition operators
Author(s)
Bibliographic Information
Cyclic phenomena for composition operators
（Memoirs of the American Mathematical Society, no. 596）
American Mathematical Society, 1997
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"January 1997, volume 125, number 596 (second of 5 numbers)"
Includes bibliographical references (p. 102-105)
Description and Table of Contents
Description
The cyclic behavior of a composition operator is closely tied to the dynamical behavior of its inducing map. Based on analysis of fixed-point and orbital properties of inducing maps, Bourdon and Shapiro show that composition operators exhibit strikingly diverse types of cyclic behavior. The authors connect this behavior with classical problems involving polynomial approximation and analytic functional equations. Features include: complete classification of the cyclic behavior of composition operators induced by linear-fractional mappings; application of linear-fractional models to obtain more general cyclicity results; and, information concerning the properties of solutions to Schroeder's and Abel's functional equations. This pioneering work forges new links between classical function theory and operator theory, and contributes new results to the study of classical analytic functional equations.
Table of Contents
Introduction Preliminaries Linear-fractional composition operators Linear-fractional models The hyperbolic and parabolic models Cyclicity: Parabolic nonautomorphism case Endnotes References.
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