Continuous refinement equations and subdivision

This paper is concerned with the study of a general class of functional equations covering as special cases the relation which defines the up-function as well as equations which arise in multiresolution analysis for wavelet construction. We discuss various basic properties of solutions to these functional equations such as regularity, polynomial containment within the space spanned by their integer shifts and their computability by subdivision algorithms. © 1993 J.C. Baltzer AG, Science Publishers.