Local algebras of two-sided convolutions on the Heisenberg group
type: Item
instance of: scholarly article
title: Local algebras of two-sided convolutions on the Heisenberg group
zbMATH Open document ID: 0876.22012
DOI: 10.1007/BF02308537
published in: Mathematical Notes
publication date: 1997-07-14T00:00:00Z
review text: Operator algebras generated by two-sided convolutions on the Heisenberg group \(H_n\) and by the operators of multiplication by continuous functions on \(\dot{H}_n\) are studied by performing a localization with respect to points of \(\dot{H}_n\). It is shown that the operators, locally equivalent to two-sided convolutions under this localization, are triples of operators of left and right convolutions, and of Euclidean convolutions as well. Composition laws for these triples are found.
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 1028518
zbMATH Keywords: third order Heisenberg group convolution composition law
zbMATH Keywords: operator algebra
author: Vladimir V. Kisil
reviewed by: Eugene Kryachko
MaRDI profile type: Publication
cites work: Q3995517
cites work: Harmonic Analysis in Phase Space. (AM-122)
cites work: Group convolution operators on standard CR-manifolds. I: Structural properties
cites work: Local behavior of two-sided convolution operators with singular kernels on the Heisenberg group
cites work: Q3897569
cites work: Q5523233
full work available at URL: https://doi.org/10.1007/bf02308537
OpenAlex ID: W2043919676
description: scientific article; zbMATH DE number 1028518