Boundedness and compactness of the spherical mean two-wavelet localization operators
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.
spherical mean two-wavelet localization operators
scientific article; zbMATH DE number 7434786
scientific article