Independent sets and lacunarity for hypergroups

Journal of the Australian Mathematical Society

Richard C. Vrem¹ 

关键词: 43 A 46;    43 A 40;   

DOI  :  10.1017/S1446788700032663

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown