Separation by characters or positive definite functions
type: Item
instance of: scholarly article
title: Separation by characters or positive definite functions
zbMATH Open document ID: 0867.43002
DOI: 10.1007/BF02574146
published in: Semigroup Forum
publication date: 1996-11-10T00:00:00Z
full work available at URL: https://eudml.org/doc/135494
review text: Let \(S\) be a commutative semigroup with neutral element and (perhaps) with involution. It is well known that in general not every positive definite function on \(S\) is a mixture of characters (already on \(\mathbb{N}_0 \times \mathbb{N}_0\) there are counterexamples). Nevertheless, the author proves that if \(a,b\in S\) and \(\sigma(a)=\sigma(b)\) for each character \(\sigma\), then necessarily \(\varphi(a)= \varphi (b)\) for each positive definite function. The proof is highly nontrivial and shows deep insight into the fascinating area of ``Harmonic analysis on semigroups''.
reviewed by: Paul Ressel
Mathematics Subject Classification ID: 43A35
zbMATH DE Number: 943671
zbMATH Keywords: separation by characters
zbMATH Keywords: harmonic analysis
zbMATH Keywords: commutative semigroup
zbMATH Keywords: positive definite function
author: Torben Maack Bisgaard
MaRDI profile type: Publication
cites work: A remark on the multidimensional moment problem
cites work: Q3755956
cites work: Extension of characters on *-semigroups
cites work: Q5829819
cites work: Q4291792
cites work: An Example of a Positive Polynomial which is not a Sum of Squares of Polynomials A Positive, but not Strongly Positive Functional
description: scientific article; zbMATH DE number 943671