Some applications of Boolean valued set theory to abstract harmonic analysis on locally compact groups
type: Item
instance of: scholarly article
title: Some applications of Boolean valued set theory to abstract harmonic analysis on locally compact groups
zbMATH Open document ID: 0582.43005
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1985-01-01T00:00:00Z
review text: The object of this paper is to extend abstract harmonic analysis on locally compact abelian groups to more general locally compact groups by using Boolean valued technique. In {\S} 2, the author gives a brief review of Boolean valued set theory. {\S} 3 contains the result: a unitary representation \(\gamma\) (\(\gamma\) : \(G\to\) the group of unitary operators of a Hilbert space H) of a locally compact group G is irreducible in a Boolean valued universe \(V^{(B)}\), where B is a Boolean algebra of projections of H with some additional property. In {\S} 4, by Boolean valued argument, the author proves that every positive definite function on G is regarded as the Fourier transform which corresponds to Bochner's well-known theorem.
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 22D10
Mathematics Subject Classification ID: 26E35
Mathematics Subject Classification ID: 03E40
Mathematics Subject Classification ID: 03G05
zbMATH DE Number: 3931683
zbMATH Keywords: Bochner theorem
zbMATH Keywords: abstract harmonic analysis
zbMATH Keywords: locally compact groups
zbMATH Keywords: Boolean valued set theory
zbMATH Keywords: unitary representation
zbMATH Keywords: Boolean algebra of projections
zbMATH Keywords: positive definite function
zbMATH Keywords: Fourier transform
author: Hirokazu Nishimura
reviewed by: Kiyoshi Iseki
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195179842
OpenAlex ID: W2071898284
DOI: 10.2977/PRIMS/1195179842
description: scientific article; zbMATH DE number 3931683