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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The measure algebra of a locally compact hypergroup
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by Charles F. Dunkl
Trans. Amer. Math. Soc. 179 (1973), 331-348
DOI: https://doi.org/10.1090/S0002-9947-1973-0320635-2

Abstract:

A hypergroup is a locally compact space on which the space of finite regular Borel measures has a convolution structure preserving the probability measures. This paper deals only with commutative hypergroups. §1 contains definitions, a discussion of invariant measures, and a characterization of idempotent probability measures. §2 deals with the characters of a hypergroup. §3 is about hypergroups, which have generalized translation operators (in the sense of Levitan), and subhypergroups of such. In this case the set of characters provides much information. Finally §4 discusses examples, such as the space of conjugacy classes of a compact group, certain compact homogeneous spaces, ultraspherical series, and finite hypergroups.
References
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Bibliographic Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 179 (1973), 331-348
  • MSC: Primary 43A10; Secondary 22A20
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0320635-2
  • MathSciNet review: 0320635