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Some Old Orthogonal Polynomials Revisited and Associated Wavelets: Two-Parameters Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets
Journal article   Peer reviewed

Some Old Orthogonal Polynomials Revisited and Associated Wavelets: Two-Parameters Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets

Sabrine Arfaoui and Anouar Ben Mabrouk
Acta applicandae mathematicae, Vol.155(1), pp.177-195
01/06/2018

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
In the present paper, new classes of wavelet functions are developed in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on two-parameters weight functions generalizing the well known Jacobi and Gegenbauer classes when relaxing the parameters. The discovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rule have been proved.

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