Designment and Traits of Quarternary Multiwavelets and Applications in Solid-State Physics and Materials Science

Abstract

Information science focuses on understanding problems from the perspective of the stakeholders involved and then applying information and other technologies as needed. New physics emerge because of the diverse new material properties which need to be explained. In this work, the notion of vector-valued multiresolution analysis and biorthogonal binary multi- tiwavelets is introduced. The existence of compactly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A new method for constructing a class of biorthogonal compactly supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory.