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Joint Meeting of AMS, DMV, and ÖMG
June 16-19, 2005
Johannes Gutenberg University
Mainz, Germany

Organizers
Volker Bach, Mainz; Klaus D. Bierstedt, DMV; Susan Friedlander, Associate Secretary, AMS

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Operators generating maximal radial cluster sets
by
José Antonio Prado-Bassas
Universidad Autónoma de Madrid (Spain)
Coauthors: Luis Bernal-González and María del Carmen Calderón-Moreno (Universidad de Sevilla)

Given a complex-valued function F defined on the unit disk D and a subset A of D, the cluster set of F along A at the point t0 of the boundary T of D is defined as follows:
CA(F, t0)={w Î
^
C
 
 : $(zn)n Ì A with zn® t0 and F(zn)®w}.
When A is the radius ending at t0, the radial cluster set of F at t0 is the set Cr(F, t0):=CA(F, t0). Several authors have studied the existence of holomorphic functions with maximal cluster sets (equal to [^(C)]).

In this talk we will present sufficient conditions on an operator T acting on H(D) to enjoy the property that the image by T of "most" functions f Î H(D) have maximal radial cluster set at any boundary point. We will also show that many classical operators have the behavior mentioned.

Date received: February 23, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqd-06.