Two Versions of Dunkl Linear Canonical Wavelet Transforms and Applications

Saifallah Ghobber () and Hatem Mejjaoli
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Saifallah Ghobber: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
Hatem Mejjaoli: Department of Mathematics, College of Sciences, Taibah University, P.O. Box 30002, Al-Madinah Al-Munawarah 42353, Saudi Arabia

Mathematics, 2025, vol. 13, issue 19, 1-35

Abstract: Among the class of generalized Fourier transformations, the linear canonical transform is of crucial importance, mainly due to its higher degrees of freedom compared to the conventional Fourier and fractional Fourier transforms. In this paper, we will introduce and study two versions of wavelet transforms associated with the linear canonical Dunkl transform. More precisely, we investigate some applications for Dunkl linear canonical wavelet transforms. Next we will introduce and develop the harmonic analysis associated with the Dunkl linear canonical wavelet packets transform. We introduce and study three types of wavelet packets along with their associated wavelet transforms. For each of these transforms, we establish a Plancherel and a reconstruction formula, and we analyze the associated scale-discrete scaling functions.

Keywords: linear canonical Dunkl transform; Dunkl linear canonical wavelet transform; Dunkl transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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