Simultaneously maximal radial cluster sets

Authors:
L. Bernal-González;M. C. Calderón-Moreno;J. A. Prado-Bassas
Affiliations:
Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain;Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain;Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain
Venue:
Journal of Approximation Theory
Year:
2005

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Abstract

In this paper, we show that for a wide class of operators T--including infinite order differential operators, and multiplication and composition operators--acting on the space H(D) of holomorphic functions in the unit disk D, we have most functions f ∈ H(D) which enjoy the property that T f has maximal radial cluster set at any boundary point.