Representations of negative definite functions on polynomial hypergroups
type: Item
instance of: scholarly article
title: Representations of negative definite functions on polynomial hypergroups
zbMATH Open document ID: 0999.43006
author: Walter R. Bloom
author: Paul Ressel
published in: Archiv der Mathematik
publication date: 2002-07-29T00:00:00Z
review text: For commutative hypergroups there exist a Bochner theorem for bounded positive definite functions as well as a Lévy-Khinchin formula for lower bounded, negative definite functions. In this paper the authors derive corresponding results for functions on polynomial hypergroups without any boundedness conditions. In this case, the representing measure and the Lévy measure \(\mu\), respectively, are positive measures on \(\mathbb{R}\) which is regarded as the space of all semicharacters. These measures are usually not unique. Moreover, algebraic conditions are given for \(\text{supp }\mu\subset \mathbb{R}_+\). Proofs are based on a transfer of the problem from polynomial hypergroups to the semigroup \((\mathbb{Z},+)\).
reviewed by: Michael Voit
Mathematics Subject Classification ID: 43A62
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 43A10
Mathematics Subject Classification ID: 43A55
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1773431
zbMATH Keywords: Lévy-Khinchin formula
zbMATH Keywords: negative definite functions
zbMATH Keywords: polynomial hypergroups
MaRDI profile type: Publication
full work available at URL: s00013-002-8253-x
OpenAlex ID: W2061187229
DOI: 10.1007/S00013-002-8253-X
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description: scientific article; zbMATH DE number 1773431