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Non-tall compact groups admit infinite Sidon sets

Published online by Cambridge University Press:  09 April 2009

M. F. Hutchinson
M. F. Hutchinson
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, N.S.W. 2006, Australia
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Abstract

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Riesz polynomials are employed to give a sufficient condition for a non-abelian compact group G to have an infinite uniformly approximable Sidon set. This condition is satisfied if G admits infinitely many pairwise inequivalent continuous irreducible unitary representations of the same degree. Consequently a compact Lie group admits an infinite Sidon set if and only if it is not semi-simple.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 4 , June 1977 , pp. 467 - 475
Copyright
Copyright © Australian Mathematical Society 1977

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