Some Ultraspheroidal Monogenic Clifford Gegenbauer Jacobi Polynomials\n and Associated Wavelets

2017/04/06 by Sabrine Arfaoui, Arfaoui, Sabrine, Anouar Ben Mabrouk +1
Mathematics · #30G35 #42B10 #44A15 #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1704.03512

openalex publication_date 2017/04/06 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In the present paper, new classes of wavelet functions are presented in the\nframework of Clifford analysis. Firstly, some classes of orthogonal polynomials\nare provided based on 2-parameters weight functions. Such classes englobe the\nwell known ones of Jacobi and Gegenbauer polynomials when relaxing one of the\nparameters. The discovered polynomial sets are next applied to introduce new\nwavelet functions. Reconstruction formula as well as Fourier-Plancherel rules\nhave been proved.\n

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