Some Ultraspheroidal Monogenic Clifford Gegenbauer Jacobi Polynomials and Associated Wavelets

被引：3
|
作者：
Arfaoui, Sabrine [1 ]
Ben Mabrouk, Anouar [2 ]
机构：
[1] Higher Inst Appl Sci & Technol Mateur, Dept Informat, St Tabarka, Mateur 7030, Tunisia
[2] Univ Kairouan, Inst Super Math Appl & Informat Kairouan, St Assad Ibn Al Fourat, Kairouan 3100, Tunisia
来源：
ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2017年 / 27卷 / 03期
关键词：
Clifford Gegenbauer Jacobi polynomials; Continuous wavelet transform; Clifford analysis; Clifford Fourier transform; Fourier-Plancherel;
D O I：
10.1007/s00006-017-0788-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页码：2287 / 2306
页数：20
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