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Toeplitz Operators for Wavelet Transform Related to the Spherical Mean Operator

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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.

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  1. Faculté des Sciences de Tunis, UR11ES23 Analyse géométrique et harmonique, Université de Tunis El Manar, 2092, Tunis, Tunisia

    Besma Amri

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  1. Besma Amri
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Amri, B. Toeplitz Operators for Wavelet Transform Related to the Spherical Mean Operator. Bull Braz Math Soc, New Series 49, 849–872 (2018). https://doi.org/10.1007/s00574-018-0083-y

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