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Mathematics
Volume 13
Issue 11
10.3390/math13111771
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A New Wavelet Transform and Its Localization Operators

by
Saifallah Ghobber
1,* and
Hatem Mejjaoli
2
1
Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
2
Department of Mathematics, College of Sciences, Taibah University, P.O. Box 30002, Al Madinah Al Munawarah 42353, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(11), 1771; https://doi.org/10.3390/math13111771
Submission received: 12 April 2025 / Revised: 22 May 2025 / Accepted: 23 May 2025 / Published: 26 May 2025
(This article belongs to the Section C: Mathematical Analysis)
Versions Notes

Abstract

In the present paper we define and study a new wavelet transformation associated to the linear canonical Dunkl transform (LCDT), which has been widely used in signal processing and other related fields. Then we define and study a class of pseudo-differential operators known as time-frequency (or localization) operators and we give criteria for its boundedness and Schatten class properties.
Keywords: linear canonical Dunkl transform; generalized wavelet transform; localization operators linear canonical Dunkl transform; generalized wavelet transform; localization operators

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MDPI and ACS Style

Ghobber, S.; Mejjaoli, H. A New Wavelet Transform and Its Localization Operators. Mathematics 2025, 13, 1771. https://doi.org/10.3390/math13111771

AMA Style

Ghobber S, Mejjaoli H. A New Wavelet Transform and Its Localization Operators. Mathematics. 2025; 13(11):1771. https://doi.org/10.3390/math13111771

Chicago/Turabian Style

Ghobber, Saifallah, and Hatem Mejjaoli. 2025. "A New Wavelet Transform and Its Localization Operators" Mathematics 13, no. 11: 1771. https://doi.org/10.3390/math13111771

APA Style

Ghobber, S., & Mejjaoli, H. (2025). A New Wavelet Transform and Its Localization Operators. Mathematics, 13(11), 1771. https://doi.org/10.3390/math13111771

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