Special affine biorthogonal wavelets on R and logarithmic regression curves

Waseem Z Lone, Firdous A Shah

In the article "Special affine multiresolution analysis and the construction of orthonormal wavelets in L 2 (R)", [Appl Anal. 2022; D.O.I: 10.1080/00036811.2022.2030723], we introduced the notion of multiresolution analysis (MRA) in the realm of the special affine Fourier transform. In continuation to the study, our aim is to present the construction of special affine biorthogonal wavelets in L 2 (R). Besides, we provide a complete characterization for the biorthogonality of the translates of the scaling functions of two special affine MRA's and the associated special affine biorthogonal wavelet families. We show that the wavelets associated with the biorthogonal special affine MRA's are also biorthogonal in nature. To extend the scope of the present study, we present the biorthogonal special affine MRA and its biorthogonal properties on a logarithmic regression curve C.