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- W2975842894 abstract "The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by Dunkl (Am Math Soc 179:331–348, 1973), Jewett (Adv Math 18(1):1–101, 1975) and Spector (Apercu de la theorie des hypergroups, (French) Analyse harmonique sur les groupes de Lie (Sem. Nancy–Strasbourg, 1973–75), Springer, New York, 1975) independently around 1972. We introduce and study several natural algebraic and analytic structures on semihypergroups, which are well-known in the case of topological groups and semigroups. In particular, we first study almost periodic and weakly almost periodic function spaces (basic properties, their relation to the compactness of the underlying space, introversion and Arens product on their duals among others). We then introduce homomorphisms and ideals, and thereby examine their behaviour (basic properties, structure of the kernel and relation of amenability to minimal ideals) in order to gain insight into the structure of a Semihypergroup itself. In the process, we further investigate where and why this theory deviates from the classical theory of semigroups." @default.
- W2975842894 created "2019-10-03" @default.
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- W2975842894 date "2019-09-28" @default.
- W2975842894 modified "2023-09-26" @default.
- W2975842894 title "Analysis on semihypergroups: function spaces, homomorphisms and ideals" @default.
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- W2975842894 doi "https://doi.org/10.1007/s00233-019-10065-6" @default.
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