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 - <p style="text-align: justify;">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.</p>