Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets  

作　　者：Sabrine Arfaoui Anouar Ben Mabrouk 

机构地区：[1]Algebra,Number Theory and Nonlinear Analysis Laboratory LR18ES15,Department of Mathematics,Faculty of Sciences,Monastir 5000,Tunisia [2]Department of Mathematics,Higher Institute of Applied Mathematics and Computer Science,Street of Assad Ibn Alfourat,Kairouan University,3100 Kairouan Tunisia [3]Department of Mathematics,Faculty of Sciences,University of Tabuk,Saudi Arabia

出　　处：《Analysis in Theory and Applications》2022年第4期394-416,共23页分析理论与应用（英文刊）

摘　　要：In the present paper,by extending some fractional calculus to the framework of Clifford analysis,new classes of wavelet functions are presented.Firstly,some classes of monogenic polynomials are provided based on 2-parameters weight functions which extend the classical Jacobi ones in the context of Clifford analysis.The discovered polynomial sets are next applied to introduce new wavelet functions.Reconstruction formula as well as Fourier-Plancherel rules have been proved.The main tool reposes on the extension of fractional derivatives,fractional integrals and fractional Fourier transforms to Clifford analysis.

关 键 词：Continuous wavelet transform Clifford analysis Clifford Fourier transform Fourier-plancherel fractional Fourier transform fractional derivatives fractional integrals fractional Clifford Fourier transform Monogenic functions. 

分 类 号：O174.2[理学—数学]