Rocky Mountain Journal of Mathematics

Spectral theorems associated with the Riemann-Liouville-Wigner localization operators

Hatem Mejjaoli and Khalifa Trimeche

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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 $.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 1 (2019), 247-281.

Dates
First available in Project Euclid: 10 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1552186961

Digital Object Identifier
doi:10.1216/RMJ-2019-49-1-247

Mathematical Reviews number (MathSciNet)
MR3921876

Zentralblatt MATH identifier
07036627

Subjects
Primary: 33E30: Other functions coming from differential, difference and integral equations 43A32: Other transforms and operators of Fourier type

Keywords
Riemann-Liouville operator Riemann-Liouville-Wigner transform localization operators admissible wavelets

Citation

Mejjaoli, Hatem; Trimeche, Khalifa. Spectral theorems associated with the Riemann-Liouville-Wigner localization operators. Rocky Mountain J. Math. 49 (2019), no. 1, 247--281. doi:10.1216/RMJ-2019-49-1-247. https://projecteuclid.org/euclid.rmjm/1552186961


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