Some generalized Clifford-Jacobi polynomials and associated spheroidal wavelets. (English) Zbl 1538.42080
Summary: 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.
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 26A33 | Fractional derivatives and integrals |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 30G35 | Functions of hypercomplex variables and generalized variables |
Keywords:
continuous wavelet transform; Clifford analysis; Clifford Fourier transform; Fourier-Plancherel; fractional Fourier transform; fractional derivatives; fractional integrals; fractional Clifford Fourier transform; monogenic functionsReferences:
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