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Uniform distribution in compact groups

Published online by Cambridge University Press:  26 February 2010

Joseph Rosenblatt
Joseph Rosenblatt
Affiliation:
Ohio State University, Coloumbus, Ohio 43210, U.S.A.
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Abstract

In a compact group G, a sequence (Fn) of finite sets is uniformly distributed if the averaging operators

are uniformly convergent to the mean for continuous complex-valued functions f. In any compact metric group, there are uniformly distributed sequences of finite sets which are determined by a metric for the group. In some compact groups, there are uniformly distributed sequences of finite sets which are determined by the algebraic structure. A necessary and sufficient condition for a sequence of finite sets to be uniformly distributed in a compact metric group is that for any metric d for G and each εG, there is a sequence of one-to-one maps pn: Fn→ Fn such that

Type
Research Article
Information
Mathematika , Volume 23 , Issue 2 , December 1976 , pp. 198 - 207
Copyright
Copyright © University College London 1976

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