Vector valued nonuniform multiresolution analysis associated with linear canonical transform

TL;DR

This paper extends the theory of multiresolution analysis associated with the linear canonical transform by introducing vector-valued nonuniform multiresolution analysis, providing conditions for wavelet existence and an algorithm for construction on local fields.

Contribution

It introduces LCT-VNUMRA, a novel framework for vector-valued nonuniform multiresolution analysis linked to the linear canonical transform, including existence conditions and construction algorithms.

Findings

Established necessary and sufficient conditions for wavelet existence.

Developed an algorithm for constructing LCT-VNUMRA on local fields.

Extended multiresolution analysis theory to nonuniform, vector-valued settings.

Abstract

A multiresolution analysis associated with linear canonical transform was defined by Shah and Waseem for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis associated with linear canonical transform (LCT-VNUMRA). 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 on local fields starting from a vector refinement mask with appropriate conditions.