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Cesàro kernels on classical groups

Part of: Abstract harmonic analysis Lie groups

Published online by Cambridge University Press:  09 April 2009

Dashan Fan
Dashan Fan
Affiliation:
Department of Mathematical Sciences University of Wisconsin-MilwaukeeMilwaukee, WI 53201USA e-mail: fan@alphal.csd.uwm.edu
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Abstract

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We study the Cesàro operator on the classical group G and give a necessary and sufficient condition on the index α = α(G) for which the operator is convergent to f(U) for any continuous function f as N → ∞. The result in this paper solves a question posed by Gong in the book Harmonic analysis on classical groups.

Keywords

Fourier seriesCesàro meansclassical groupLebesgue constant.

MSC classification

Secondary: 43A55: Summability methods on groups, semigroups, etc. 43A50: Convergence of Fourier series and of inverse transforms 43A80: Analysis on other specific Lie groups 22E20: General properties and structure of other Lie groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 3 , December 1997 , pp. 364 - 389
Copyright
Copyright © Australian Mathematical Society 1997

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