Analyse harmonique sur les groupes de Heisenberg généralisés
type: Item
instance of: scholarly article
title: Analyse harmonique sur les groupes de Heisenberg généralisés
zbMATH Open document ID: 0543.22004
DOI: 10.1007/BF01536906
author: Marc Burger
published in: Monatshefte für Mathematik
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178188
review text: Let \(G=(X_ 1,X_ 2,X_ 3)_ B\) be the generalized Heisenberg group as defined by \textit{H. Reiter} in [Comment. Math. Helv. 49, 333-364 (1974; Zbl 0292.43007)]. Under some natural conditions on G involving not the separability, we clarify the unitary irreducible representations of G. We prove a Fourier inversion formula and determine a space of functions \(\phi\) on G for which \(\pi\) (\(\phi)\) is a Hilbert-Schmidt operator for every irreducible representation \(\pi\) of G.
Mathematics Subject Classification ID: 22D10
zbMATH DE Number: 3863502
zbMATH Keywords: generalized Heisenberg group
zbMATH Keywords: unitary irreducible representations
zbMATH Keywords: Fourier inversion formula
MaRDI profile type: Publication
cites work: Operators arising from representations of nilpotent Lie groups
cites work: Unitary representations of group extensions. I
cites work: \(L^ 1-\)harmonic analysis on semi-direct products of abelian groups
cites work: Q5550080
cites work: Über den Satz von Wiener und lokalkompakte Gruppen
cites work: Sur certains groupes d'opérateurs unitaires
OpenAlex ID: W364795460
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description: scientific article; zbMATH DE number 3863502