Vector-valued Nonuniform Multiresolution Analysis Associated with Linear Canonical Transform Domain

Abstract

A generalization of Mallat’s classical multiresolution analysis, based on the theory of spectral

pairs, was considered in two articles by Gabardo and Nashed. In this setting, the associated translation set

is no longer a discrete subgroup of R but a spectrum associated with a certain one-dimensional spectral

pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniformmultiresolution analysis associated with linear canonical transform (LCT-VNUMRA) where the associated subspace V0 of the function space L R, C has an orthonormal basis  We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of vector-valued nonuniform multiresolution analysis starting from a vectorrefinemnt mask with appropriate conditions