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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Abstract

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

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

Dates
First available in Project Euclid: 24 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1514084424

Digital Object Identifier
doi:10.1216/RMJ-2017-47-7-2179

Mathematical Reviews number (MathSciNet)
MR3748227

Zentralblatt MATH identifier
1381.42010

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

Keywords
Riemann-Liouville transform windowed Fourier transform localization operator trace formula

Citation

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. https://projecteuclid.org/euclid.rmjm/1514084424


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