Computational Methods and Function Theory 3 (2003), No. 1, 285--297
Copyright Heldermann Verlag 2003
Luis Bernal-González
lbernal@us.es, Departamento de Análisis Matemático, Facultad de Matemáticas, Apdo. 1160, Avenida Reina Mercedes, 41080 Sevilla, Spain.
María C. Calderón-Moreno
mccm@us.es, Departamento de Análisis Matemático, Facultad de Matemáticas, Apdo. 1160, Avenida Reina Mercedes, 41080 Sevilla, Spain.
Wolfgang Luh
luh@uni-trier.de, Universität Trier, Fachbereich Mathematik, 54286 Trier, Germany.
In this paper generalized Riesz methods (R, p, M) of summability are considered. We prove that, to each open subset O of the complex plane C with adequate topological properties and to each sequence {Pn} of subsets of the complex plane tending to infinity, we can associate a corresponding P-regular (R, p, M)-method so that the geometric series and a certain trigonometric series become universal in the sense that its (R, p, M)-transforms approximate any member of certain spaces of holomorphic functions or measurable functions.
Keywords: Riesz method, universal function, geometric series, trigonometric series, P-regularity.
MSC 2000: Primary 30E10; Secondary 40C05, 40G99, 42A10.
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