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Volume 38, Issue 4
Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets

Sabrine Arfaoui & Anouar Ben Mabrouk

DOI: 10.4208/ata.OA-2019-0037

Anal. Theory Appl., 38 (2022), pp. 394-416.

Published online: 2023-01

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  • 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.

  • Keywords

Continuous wavelet transform, Clifford analysis, Clifford Fourier transform, Fourier-plancherel, fractional Fourier transform, fractional derivatives, fractional integrals, fractional Clifford Fourier transform, Monogenic functions.

  • AMS Subject Headings

26A33, 42A38, 42B10, 44A15, 30G35

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-38-394, author = {Arfaoui , Sabrine and Mabrouk , Anouar Ben}, title = {Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {38}, number = {4}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2019-0037}, url = {http://global-sci.org/intro/article_detail/ata/21356.html} }
TY - JOUR T1 - Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets AU - Arfaoui , Sabrine AU - Mabrouk , Anouar Ben JO - Analysis in Theory and Applications VL - 4 SP - 394 EP - 416 PY - 2023 DA - 2023/01 SN - 38 DO - http://doi.org/10.4208/ata.OA-2019-0037 UR - https://global-sci.org/intro/article_detail/ata/21356.html KW - Continuous wavelet transform, Clifford analysis, Clifford Fourier transform, Fourier-plancherel, fractional Fourier transform, fractional derivatives, fractional integrals, fractional Clifford Fourier transform, Monogenic functions. AB -

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.

Arfaoui , Sabrine and Mabrouk , Anouar Ben. (2023). Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets. Analysis in Theory and Applications. 38 (4). 394-416. doi:10.4208/ata.OA-2019-0037
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