Operator covariant transform and local principle
type: Item
instance of: scholarly article
title: Operator covariant transform and local principle
zbMATH Open document ID: 1298.81111
DOI: 10.1088/1751-8113/45/24/244022
published in: Journal of Physics A: Mathematical and Theoretical
publication date: 2012-07-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1201.1749
full work available at URL: 1201.1749v1.pdf
Mathematics Subject Classification ID: 81R15
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 47L55
Mathematics Subject Classification ID: 81T05
zbMATH DE Number: 6056035
zbMATH Keywords: operator localization
zbMATH Keywords: operator convariant transform
zbMATH Keywords: nilpotent Lie groups
Wikidata QID: Q59902479
author: Vladimir V. Kisil
MaRDI profile type: Publication
OpenAlex ID: W3104523149
arXiv ID: 1201.1749
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review text: \textit{I. B. Simonenko} [Izv. Akad. Nauk SSSR, Ser. Mat. 29, 567--586, 757--782 (1965; Zbl 0146.13101)] introduced the localization technique to the theory of operators to study singular integral operators that are convolutions on the Euclidean group. In this paper, the author presents a different point of view on the original works of Simonenko in the context of the covariant transform. The new interpretation highlights the role of groups in the constructions, and links a certain geometrical meaning of locality with a homogeneous structure of nilpotent Lie groups. Thus, it allows one to make a straightforward modification of the localization technique for non-commutative nilpotent Lie groups. The key role is played by the one-parameter group of automorphisms realized as dilations.
reviewed by: Miyeon Kwon
description: scientific article; zbMATH DE number 6056035