Multiresolution Analysis and Multivariate Approximation of Smooth Signals in CB(Rd

Abstract

In this paper we derive rates of approximation for a class of linear operators on \(C_B({\bf R}^d)\) associated with a multiresolution analysis \(\{ V_n\}_{n\in{\bf Z}}.\) We show that for a uniformly bounded sequence of linear operators \(\{T_n\}_{n\in{\bf Z}}\) satisfying \(T_n f\equiv f\) on the subspace \(V_n\cap C_B({\bf R}^d),\) a lower bound for the approximation order is determined by the number of vanishing moments of a prewavelet set. We consider applications to extensions of generalized projection operators as well as to sampling series.