Abstract: We consider expansion series in terms of scaled translates ?(h-1z-k) of a basic function ?. The coefficients are given by sampled values Rhf(kh) where Rhf are averaging operators obtained by convolutions f? dvh. Examples of such expansions have been used in finite element approximations and sampling theory. More recently, they have received considerable attention in wavelet analysis. In this context, the basic functions ? are named scaling functions. They generate nice decompositions of L2(R) which are called multiresolution analysis of L2(R). This article concerns itself with the convergence of these series in the Sobolev H'-norm. Results already known in the finite element context are extended for basic functions not necessarely having compact support. Besides a regularity condition, ? is supposed to satisfy the so called m-criterion of convergence. In order to obtain approximations with accuracy O(hm+1-?), ? and must also be connected by a moment relation. Emphasis is placed on expansions in a multiresolution analysis of L2(R). We give special attention to those cases where the coefficients are given by discrete convolutions. Some examples, including sampling series, interpolation and approximate orthogonal projections, are discussed Ver menos