Year: 2022
Author: Sabrine Arfaoui, Anouar Ben Mabrouk
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 4 : pp. 394–416
Abstract
In the present paper, by extending some fractional calculus to the framework of Clifford analysis, new classes of wavelet functions are presented. Firstly, some classes of monogenic polynomials are provided based on 2-parameters weight functions which extend the classical Jacobi ones in the context of Clifford analysis. The discovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rules have been proved. The main tool reposes on the extension of fractional derivatives, fractional integrals and fractional Fourier transforms to Clifford analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2019-0037
Analysis in Theory and Applications, Vol. 38 (2022), Iss. 4 : pp. 394–416
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Continuous wavelet transform Clifford analysis Clifford Fourier transform Fourier-plancherel fractional Fourier transform fractional derivatives fractional integrals fractional Clifford Fourier transform Monogenic functions.