Quasi-interpolation in shift invariant spaces

Let s greater than or equal to 1 be an integer, phi : R-s --> R be a compac tly supported function, and S(phi) denote the linear span of {phi>(*) over bar *(.- k) : k epsilon Z(s)}. We consider the problem of approximating a c ontinuous function f: R-s --> R on compact subsets of R-s from the classes S(phi>(*) over bar * (h.)), h > 0, based on samples of the function at scat tered sites in R-s. We demonstrate how classical polynomial inequalities le ad to the construction of local, quasi-interpolatory operators for this pur pose, (C) 2000 Academic Press.