Moment problems on subsemigroups of \({\mathbb{N}{}}^ k_ 0\) and \({\mathbb{Z}{}}^ k\)
type: Item
instance of: scholarly article
title: Moment problems on subsemigroups of \({\mathbb{N}{}}^ k_ 0\) and \({\mathbb{Z}{}}^ k\)
zbMATH Open document ID: 0757.43003
DOI: 10.1007/BF03025764
author: N. Sakakibara
published in: Semigroup Forum
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/135186
review text: Let \(S\) be an abelian semigroup with involution \(*\), and let \(S^*\) be its set of \(*\)- semicharacters (non-zero \(*\)-homomorphisms of \(S\) into \(\mathbb{C}\)). We call \(S\) semiperfect if every positive definite function \(\phi\) on \(S\) can be represented by the form \(\phi(s)=\int_{S^*}\chi(s)d\mu(\chi)\) where \(\mu\) is a bounded Radon measure on \(S^*\); further \(S\) is said to be perfect if the representing measure \(\mu\) is unique. In this paper it is shown that all non-trivial semiperfect subsemigroups of \(\mathbb{Z}^ k\) (with the identity involution) are singly generated and are never perfect.
reviewed by: John W.Baker
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 22A20
Mathematics Subject Classification ID: 20M15
zbMATH DE Number: 64386
zbMATH Keywords: abelian semigroup with involution
zbMATH Keywords: semicharacters
zbMATH Keywords: positive definite function
zbMATH Keywords: semiperfect subsemigroups
MaRDI profile type: Publication
cites work: A remark on the multidimensional moment problem
cites work: Q3755956
cites work: Characterization of perfect involution groups.
cites work: The two-sided complex moment problem
cites work: Unique disintegration of arbitrary positive definite functions on \(*\)- divisible semigroups
cites work: Orthogonal Laurent polynomials and the strong Hamburger moment problem
cites work: Perfectness of certain subsemigroups of the perfect semigroup
cites work: Q5845997
OpenAlex ID: W1981859792
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description: scientific article; zbMATH DE number 64386