Affiliation:
1. Department of Mathematics, University of Kashmir, South Campus, Anantnag, Jammu and Kashmir, India
Abstract
In the article ?Special affine multiresolution analysis and the construction
of orthonormal wavelets in L2(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 L2(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 .
Publisher
National Library of Serbia