L(P)-APPROXIMATION BY CERTAIN PROJECTION OPERATORS

We estimate the L(p)(R(d))_approximation rate (1 less-than-or-equal-to p less-than-or-equal-to infinity) provided dilates of an orthogonal p rojection operator of L2(R(d)) onto a space generated by shifts of a f unction which has a polynomial decay rate at infinity and has stable s hifts. To this end we employ a quasi-interpolation scheme and invoke W iener's lemma. In particular, this paper provides further substantiati on to one of the fundamental properties of refinable functions: the co nnection between smoothness and approximation order. (C) 1994 Academic Press, Inc.