Boundedness and compactness of the spherical mean two-wavelet localization operators
type: Item
instance of: scholarly article
title: Boundedness and compactness of the spherical mean two-wavelet localization operators
zbMATH Open document ID: 1491.44003
author: Hatem Mejjaoli
author: Slim Omri
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2021-11-29T00:00:00Z
review text: Spherical means have been studied by several authors. Harmonic functions are characterized by their spherical mean values. The classic book [\textit{F. John}, Plane waves and spherical means applied to partial differential equations. New York, NY: Interscience Publishers (1955; Zbl 0067.32101)] deals with various applications of the spherical means to the theory of partial differential equations. In this paper, the authors use the properties of the Fourier transform associated with the spherical mean operator to study the boundedness and compactness of the two-wavelet localization operators associated to the spherical mean operator. The extension of one wavelet to two wavelets gives the extra degree of flexibility in signal analysis and imaging when the localization operators are used as time-varying filters. Some results of the harmonic analysis associated with the spherical mean operator and Schatten-von Neumann classes are given. The two-wavelet localization operators in the setting of the spherical mean operator are considered. The Schatten-von Neumann properties of these two localization wavelet operators are established, for trace class spherical mean two-wavelet localization operators, the traces and the trace class norm inequalities are presented.
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 42B15
zbMATH DE Number: 7434786
zbMATH Keywords: spherical mean operator
zbMATH Keywords: spherical mean two-wavelet localization operators
zbMATH Keywords: Schatten-von Neumann class
reviewed by: S. L. Kalla
MaRDI profile type: Publication
full work available at URL: s00574-020-00241-6
OpenAlex ID: W3123214953
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DOI: 10.1007/S00574-020-00241-6
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description: scientific article; zbMATH DE number 7434786