Cyclic Phenomena for Composition Operators
Paul Bourdon · Joel H. Shapiro
Jan 1997 · American Mathematical Society: Memoirs of the American Mathematical Society Book 596 · American Mathematical Soc.
Ebook
105
Pages
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About this ebook
The cyclic behaviour of a composition operator is closely tied to the dynamical behaviour 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 behaviour. The authors connect this behaviour with classical problems involving polynomial approximation and analytic 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.
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