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2019 Spectral theorems associated with the Riemann-Liouville-Wigner localization operators
Hatem Mejjaoli, Khalifa Trimeche
Rocky Mountain J. Math. 49(1): 247-281 (2019). DOI: 10.1216/RMJ-2019-49-1-247

Abstract

We introduce the notion of localization operators associated with the Riemann-Liouville-Wigner transform, and we give a trace formula for the localization operators associated with the Riemann-Liouville-Wigner transform as a bounded linear operator in the trace class from $L^{2}(d\nu _{\alpha })$ into $L^{2}(d\nu _{\alpha })$ in terms of the symbol and the two admissible wavelets. Next, we give results on the boundedness and compactness of localization operators associated with the Riemann-Liouville-Wigner transform on $L^{p}(d\nu _{\alpha })$, $1 \leq p \leq \infty $.

Citation

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Hatem Mejjaoli. Khalifa Trimeche. "Spectral theorems associated with the Riemann-Liouville-Wigner localization operators." Rocky Mountain J. Math. 49 (1) 247 - 281, 2019. https://doi.org/10.1216/RMJ-2019-49-1-247

Information

Published: 2019
First available in Project Euclid: 10 March 2019

zbMATH: 07036627
MathSciNet: MR3921876
Digital Object Identifier: 10.1216/RMJ-2019-49-1-247

Subjects:
Primary: 33E30, ‎43A32

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 1 • 2019
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