Quasi-interpolation in shift invariant spaces

Abstract

Let s≤1 be an integer, φ: Rs→R be a compactly supported function, and S(φ) denote the linear span of {φ(·-k):kεZs}. We consider the problem of approximating a continuous function f:Rs→R on compact subsets of Rs from the classes S(φ(h·)), h0, based on samples of the function at scattered sites in Rs. We demonstrate how classical polynomial inequalities lead to the construction of local, quasi-interpolatory operators for this purpose. © 2000 Academic Press.