J Austral Math Soc Ser A 50 pp171--188, 1991.

Independent Sets and Lacunarity for Hypergroups

Richaed C. Vrem

Abstract

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 L 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 L are equivalent. Several applications are provided, primarily to questions regarding lacunarity on compact groups.

1980 AMS Subject Classification (1985 Revision): 43A46, 43A40

Browse the article

Authors

Richard C. Vrem

Humboldt State University, Arcata, California 95521, U.S.A.