A NONLINEAR OPERATOR RELATED TO SCALING FUNCTIONS AND WAVELETS

This paper studies a certain nonlinear operator T from L(2)(R) to itse lf under which every scaling function is a fixed point, The iterations T(n)f of T on any L(2)-function f with the Riesz basis property are i nvestigated; they turn out to be the subdivision-scheme iterates of f with weights depending on f only. The paper gives conditions far conve rgence of T(n)f to a limit in different topologies and studies the reg ularity oi the limit functions. The results are illustrated with examp les.