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Some Ultraspheroidal Monogenic Clifford Gegenbauer Jacobi Polynomials and Associated Wavelets
Journal article   Peer reviewed

Some Ultraspheroidal Monogenic Clifford Gegenbauer Jacobi Polynomials and Associated Wavelets

Sabrine Arfaoui and Anouar Ben Mabrouk
Advances in applied Clifford algebras, Vol.27(3), pp.2287-2306
01/09/2017

Abstract

Mathematics Mathematics, Applied Physical Sciences Physics Physics, Mathematical Science & Technology
In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on 2-parameters weight functions. Such classes englobe the well known ones of Jacobi and Gegenbauer polynomials when relaxing one of the parameters. The discovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rules have been proved.

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