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On the dual of a commutative signed hypergroup

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Abstract

Signed hypergroups are convolution structures similar to hypergroups, though being not necessarily positivity-preserving. We prove a generalized Plancherel theorem for positive definite measures on a commutative signed hypergroup, with an analogue of the classical Plancherel theorem as a special case. Moreover, signed hypergroups with subexponential growth are studied. As an application, the dual of the Laguerre convolution structure on ℝ+ is determined.

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  1. Mathematisches Institut, Technische Universität München, Arcisstr. 21, 80333, München, Germany

    Margit Rösler

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  1. Margit Rösler
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Rösler, M. On the dual of a commutative signed hypergroup. Manuscripta Math 88, 147–163 (1995). https://doi.org/10.1007/BF02567812

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  • DOI: https://doi.org/10.1007/BF02567812

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