Pull-back properties of moment functions and a generalization of Bochner-Weil's theorem
type: Item
instance of: scholarly article
title: Pull-back properties of moment functions and a generalization of Bochner-Weil's theorem
zbMATH Open document ID: 0839.43006
DOI: 10.1007/BF01450496
published in: Mathematische Annalen
publication date: 1996-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/165262
review text: Let \((\mathbb{S}, +,*)\) be a topological Abelian *-semigroup, let \(\mathbb{S}^*\) be the set of semicharacters which are bounded with respect to a function \(\gamma\), called absolute value, and let \(\mathbb{S}^*_c\) denote the subset of continuous \(\gamma\)-bounded semicharacters. Define in the usual way for a nonnegative Radon measure \(\lambda\) on \(\mathbb{S}^*\) the generalized Laplace transform \(\widehat \lambda (s)\), \(s \in \mathbb{S}\). The aim of the paper under review is to prove for a large class of *-semigroups with identity a Bochner-Weil-theorem. These *-semigroups, called \(\gamma\)-admissible, generalize e.g. discrete semigroups, locally compact Abelian groups, the semigroup ([0,1], min). The main results are a characterization of \(\mathbb{S}_c^*\) within \(\mathbb{S}^*\) (Theorem A) and of generalized Laplace transforms (Theorem B). Theorems \(C-E\) contain Bochner-Weil theorems for interesting special cases of \(\gamma\)-admissible *-semigroups.
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 43A30
Mathematics Subject Classification ID: 43A32
zbMATH DE Number: 701008
zbMATH Keywords: semicharacters
zbMATH Keywords: generalized Laplace transform
zbMATH Keywords: *-semigroups
zbMATH Keywords: Bochner-Weil-theorem
zbMATH Keywords: discrete semigroups
zbMATH Keywords: locally compact Abelian groups
author: El-Hassan Youssfi
reviewed by: Wilfried Hazod
MaRDI profile type: Publication
cites work: Exponentially bounded positive definite functions
cites work: Une démonstration du théorème de Bochner-Weil par discrétisation du groupe. (A proof of the Bochner-Weil theorem by discretization of the group)
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description: scientific article; zbMATH DE number 701008