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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Continuous measures and lacunarity on hypergroups


Author: Richard C. Vrem
Journal: Trans. Amer. Math. Soc. 269 (1982), 549-556
MSC: Primary 43A46; Secondary 22A10, 43A05
MathSciNet review: 637708
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Abstract: The relationship between measures on a compact hypergroup $ K$ whose Fourier-Stieltjes transforms vanish at infinity and the space $ {M_c}(K)$ of continuous measures is studied. Examples are provided of measures $ \mu $ with $ \hat \mu $ vanishing at infinity and $ \mu \in {M_c}(K)$. Sufficient conditions are given for $ \hat \mu \in {c_0}(\hat K)$ to imply $ \mu \in {M_c}(K)$. An investigation of Helson sets on compact abelian hypergroups is initiated and the study of Sidon sets on compact abelian hypergroups is continued. A class of compact abelian hypergroups is shown to have no infinite Helson sets and no infinite Sidon sets. This result generalizes results of D. L. Ragozin and D. Rider on central Sidon sets for compact connected Lie groups.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0637708-2
PII: S 0002-9947(1982)0637708-2
Article copyright: © Copyright 1982 American Mathematical Society