COORDINATE ORDER OF APPROXIMATION BY FUNCTIONAL-BASED APPROXIMATION OPERATORS

We study coordinatewise L(p) approximation by a fairly general class of linear operators that includes quasi-intrpolants and, like these, is based on a globally supported basis function and a globally supported linear functional of general form with certain mild decay conditions imposed on the basis function and the functional involved, In this quite general setting we show that the approximation power provided by a quasi-interpolant and other functional-based operators is equivalent to the polynomial reproducing property possessed by it. (C) 1995 Academic Press, Inc.