An Equivalence Relation between Multiresolution Analysis ofL2(R)

Abstract This paper is concerned with the development of an equivalence relation between two multiresolution analysis of L 2 ( R ). The relation called unitary equivalence is created by the action of a unitary operator in such a way that the multiresolution structure and the decomposition and reconstruction algorithms remain invariant. A characterization in terms of the scaling functions of the multiresolution analysis is given. Distinct equivalence classes of multiresolution analysis are derived. Finally, we prove that B-splines give rise to nonequivalent examples.