Convolution on homogeneous groups
type: Item
instance of: scholarly article
title: Convolution on homogeneous groups
zbMATH Open document ID: 1203.43008
author: Susana Coré
author: Daryl Geller
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-07-20T00:00:00Z
review text: Using methods from wavelet theory due to \textit{M. Frazier} and \textit{B. Jawerth} [Indiana Univ. Math. J. 34, 777--799 (1985; Zbl 0551.46018)] the authors give interesting characterizations of convolutions on homogeneous groups. While the presentation in the paper is (necessarily) rather technical, the results are natural! Hence the authors are right to expect more results for operators on homogeneous groups proved along these lines. For those who know some of the analysis on homogeneous groups, here a bit more. On \(G\) the homogeneous norm is taken and the basic space for working with the Fourier transform is the Schwartz space on \(G\) with functions having all moments vanishing. Consider functions whose derivatives decay as those of homogeneous functions of degree \(j\). Take the inverse Fourier transform of these functions. Convolution of two elements in these spaces each of ``homogeneity'' degree \(j_1\) and \(j_2\), respectively, yields a function of ``homogeneity degree'' of degree \(j_1+ j_2\).
reviewed by: Niels Jacob
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 43A25
Mathematics Subject Classification ID: 43A32
zbMATH DE Number: 5757969
zbMATH Keywords: homogeneous group
zbMATH Keywords: convolution
zbMATH Keywords: Fourier transform
zbMATH Keywords: homogeneous distributions
zbMATH Keywords: wavelets
zbMATH Keywords: Heisenberg group
zbMATH Keywords: multipliers
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.04.077
OpenAlex ID: W2093939787
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DOI: 10.1016/J.JMAA.2010.04.077
description: scientific article; zbMATH DE number 5757969