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Toeplitz Operators for Wavelet Transform Related to the Spherical Mean Operator

  • Besma Amri
Article
  • 33 Downloads

Abstract

We define wavelets and wavelet transforms associated with spherical mean operator. We establish a Plancherel theorem, orthogonality property and inversion formula for the wavelet transform. Next, we define the Toeplitz operators \(\mathfrak {T}_{\varphi ,\psi }(\sigma )\) associated with two wavelets \(\varphi ,\psi \) and with symbol \(\sigma .\) We establish the boundedness and compactness of these operators. Last, we define the Schatten-von Neumann class \(S^p\ ;\ p\in \ [1,+\infty ],\) and we show that the Toeplitz operators belong to the class \(S^p\) and we prove a formula of trace.

Keywords

Orthonormal basis Hilbert Schmidt operator Frequency localization Wavelet transform Toeplitz operator Spherical mean operator Fourier transform 

Mathematics Subject Classification

42A38 44A35 

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Copyright information

© Sociedade Brasileira de Matemática 2018

Authors and Affiliations

  1. 1.Faculté des Sciences de Tunis, UR11ES23 Analyse géométrique et harmoniqueUniversité de Tunis El ManarTunisTunisia

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