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
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
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