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Independent sets and lacunarity for hypergroups

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Richard C. Vrem
Richard C. Vrem
Affiliation:
Humboldt State UniversityArcata, California 95521, U.S.A.
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Abstract

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Sets of independence are studied for compact abelian hypergroups and they are used, along with Riesz products, to investigate lacunarity questions on the dual object. It is shown that bounded Stechkin sets are always Sidon and that every bounded infinite subset of the dual contains an infinite Sidon set which is also a Λ set. Independent sets are shown to always be Sidon and a necessary condition for Sidonicity is provided. A result of Pisier is used to show that for compact non-abelian groups Sidon and central Λ are equivalent. Several applications are provided, primarily to questions regarding lacunarity on compact groups.

MSC classification

Secondary: 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) 43A40: Character groups and dual objects
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 2 , April 1991 , pp. 171 - 188
Copyright
Copyright © Australian Mathematical Society 1991

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