Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets (Analysis in Theory and Applications, 2023)
In the present paper, by extending some fractional calculus to the framework of Clifford analysis, new classes of wavelet functions are presented. Firstly, someclasses of monogenic polynomials are provided based on 2-parameters weight functions which extend the classical Jacobi ones in the context of Clifford analysis. Thediscovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rules have been proved. The maintool 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.