Cyclic Phenomena for Composition Operators

Paul S. Bourdon and Joel H. Shapiro

Memoirs, Amer. Math. Soc. #596, January 1997

Abstract: We undertake a systematic study of cyclic phenomena for composition operators. Our work shows that composition operators exhibit strikingly diverse types of cyclic behavior, and it connects this behavior with classical problems involving complex polynomial approximation and analytic functional equations.

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