Rocky Mountain Journal of Mathematics

Localization operators for the windowed Fourier transform associated with singular partial differential operators

Nadia Ben Hamadi

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We introduce the windowed Fourier transform connected with some singular partial differential operators defined on the half plane $\left [0,+\infty \right [\,\times \mathbb {R}$. Then, we investigate localization operators and show that these operators are not only bounded but also in the Shatten-von Neumann class. We give a trace formula when the symbol function is a nonnegative function.

Article information

Rocky Mountain J. Math., Volume 47, Number 7 (2017), 2179-2195.

First available in Project Euclid: 24 December 2017

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Zentralblatt MATH identifier

Primary: 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 65R10: Integral transforms

Riemann-Liouville transform windowed Fourier transform localization operator trace formula


Hamadi, Nadia Ben. Localization operators for the windowed Fourier transform associated with singular partial differential operators. Rocky Mountain J. Math. 47 (2017), no. 7, 2179--2195. doi:10.1216/RMJ-2017-47-7-2179.

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