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Weighted p-Sidon sets

Part of: Abstract harmonic analysis Lie groups

Published online by Cambridge University Press:  09 April 2009

K. E. Hare  and
D. C. Wilson
K. E. Hare
Affiliation:
Department of Pure Mathematics University of WaterlooWaterloo OntarioCanadaN2L 3G1 e-mail: kehare@math.waterloo.edu
D. C. Wilson
Affiliation:
School of Applied Science Monash UniversityChurchill VIC 3842Australia e-mail: david.wilson@sci.monash.edu.au
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Abstract

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A weighted generalization of a p-Sidon set, called an (a, p)-Sidon set, is introduced and studied for infinite, non-abelian, connected, compact groups G. The entire dual object Ĝ is shown never to be central (p − 1, p)-Sidon for 1 ≦ p < 2, nor central (1 + ε, 2)-Sidon for ε > 0. Local (p, p)-Sidon sets are shown to be identical to local Sidon sets. Examples are constructed of infinite non-Sidon sets which are central (2p − 1, p)-Sidon, or (p − 1, p)-Sidon, for 1 < p < 2. Full m-fold FTR sets are proved not to be central (a, 2m/(m + 1))-Sidon for any a > 1.

Keywords

Sidon setlacunary setrepresentations of compact groups.

MSC classification

Secondary: 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) 43A80: Analysis on other specific Lie groups 22E46: Semisimple Lie groups and their representations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 1 , August 1996 , pp. 73 - 95
Copyright
Copyright © Australian Mathematical Society 1996

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