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New type of monogenic polynomials and associated spheroidal wavelets (1704.03498v1)
Published 6 Apr 2017 in math.CA, math-ph, and math.MP
Abstract: In the present work, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of new monogenic polynomials are provided based on 2-parameters weight functions. Such classes extend the well known Jacobi-Gegenbauer ones. The discovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rules have been proved.