On the representation of nuclear Lie groups
type: Item
instance of: scholarly article
title: On the representation of nuclear Lie groups
zbMATH Open document ID: 0859.46029
DOI: 10.1007/BF01194165
published in: Archiv der Mathematik
publication date: 1996-11-22T00:00:00Z
review text: The author gives a satisfactory solution to a question of I. M. Gelfand and N. Y. Vilenkin on infinite-dimensional harmonic analysis. They introduced the notion of nuclear Lie group and provided a concrete determination of the continuous unitary representation of such a group in case the underlying locally convex space is nuclear and metrizable. Utilizing Fourier transform of cylindrical probabilities and radonifying bornologies the author is able to give a concrete determination in the general case.
Mathematics Subject Classification ID: 46G12
Mathematics Subject Classification ID: 46A11
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 46A17
zbMATH DE Number: 937041
zbMATH Keywords: infinite-dimensional harmonic analysis
zbMATH Keywords: nuclear Lie group
zbMATH Keywords: continuous unitary representation
zbMATH Keywords: locally convex space
zbMATH Keywords: metrizable
zbMATH Keywords: Fourier transform of cylindrical probabilities
zbMATH Keywords: radonifying bornologies
author: H. Hogbe Nlend
reviewed by: H. Hogbe Nlend
MaRDI profile type: Publication
cites work: Q4052400
full work available at URL: https://doi.org/10.1007/bf01194165
OpenAlex ID: W2087430572
description: scientific article; zbMATH DE number 937041