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Some Ultraspheroidal Monogenic Clifford Gegenbauer Jacobi Polynomials and Associated Wavelets

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Abstract

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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Authors and Affiliations

  1. Department of Informatics, Higher Institute of Applied Sciences and Technology of Mateur, Street of Tabarka, 7030, Mateur, Tunisia

    Sabrine Arfaoui

  2. Institut Superieur des Mathematiques Appliquées et de l’Informatique de Kairouan, Université de Kairouan, Street of Assad Ibn Al Fourat, 3100, Kairouan, Tunisia

    Anouar Ben Mabrouk

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  1. Sabrine Arfaoui
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  2. Anouar Ben Mabrouk
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Correspondence to Sabrine Arfaoui.

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Communicated by Eckhard Hitzer

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Arfaoui, S., Ben Mabrouk, A. Some Ultraspheroidal Monogenic Clifford Gegenbauer Jacobi Polynomials and Associated Wavelets. Adv. Appl. Clifford Algebras 27, 2287–2306 (2017). https://doi.org/10.1007/s00006-017-0788-9

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