ARFAOUI Sabrine and BEN MABROUK Anouar, “Some Old Orthogonal Polynomials Revisited and Associated Wavelets: Two-Parameters Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets”, In the present paper, new classes of wavelet functions are developed in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on two-parameters weight functions generalizing the well known Jacobi and Gegenbauer classes when relaxing the parameters. The discovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rule have been proved., Acta Applicandae Mathematicae, 155:1 (2018), 177-195
ARFAOUI Sabrine and BEN MABROUK Anouar, “Some Ultraspheroidal Monogenic Clifford Gegenbauer Jacobi Polynomials and Associated Wavelets”, 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., Advances in Applied Clifford Algebras, 27:3 (2017), 2287–2306
Sabrine Arfaoui, Imen Rezgui and Anouarc Ben Mabrouk, Wavelet Analysis on the Sphere: Spheroidal Wavelets, The goal of this monograph is to develop the theory of wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials., 978-3110481891, De Gruyter, 2017
