Finite Biorthogonal Transforms and Multiresolution Analyses on Intervals

Abstract

In this dissertation a class of biorthogonal transformations for finite strings of data are described. These transformations are modifications of matrices corresponding to dual multiresolution analyses over the real line. A construction of biorthogonal multiresolution analyses over a finite interval based on the scaling coefficients is demonstrated. Regularity properties are explored and numerical examples with figures are provided.