Bochner's theorem for finite-dimensional conelike semigroups
type: Item
instance of: scholarly article
title: Bochner's theorem for finite-dimensional conelike semigroups
zbMATH Open document ID: 0790.43008
DOI: 10.1007/BF01445113
author: Paul Ressel
published in: Mathematische Annalen
publication date: 1994-03-23T00:00:00Z
full work available at URL: https://eudml.org/doc/165093
review text: A subset \(S\) of some real vector space \(V\) is called conelike, if for every \(s \in S\) there exists a number \(a(s) \in \mathbb{R}_ +\) such that \(\alpha s \in S\) for all \(\alpha \geq a(s)\). If \(S\) is also a semigroup and \(V\) is of finite dimension, we can prove the following extension of Bochner's classical theorem: Each bounded continuous positive definite function on \(S\) is a mixture of continuous characters. These continuous characters are identified in terms of a canonically associated subspace of \(V\) and the dual cone of the hermitian part of \(S\). We then give a probabilistic application.
reviewed by: Paul Ressel
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 43A30
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 537260
zbMATH Keywords: positive definite function
zbMATH Keywords: continuous characters
MaRDI profile type: Publication
cites work: Q3755956
cites work: Q4751537
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)
cites work: De Finetti-type theorems: An analytical approach
description: scientific article; zbMATH DE number 537260