Lp-Approximation by Certain Projection Operators

We estimate the Lp(Rd)-approximation rate (1≤p≤∞) provided dilates of an orthogonal projection operator of L2(Rd) onto a space generated by shifts of a function which has a polynomial decay rate at infinity and has stable shifts. To this end we employ a quasi-interpolation scheme and invoke Wiener′s lemma. In particular, this paper provides further substantiation to one of the fundamental properties of refinable functions: the connection between smoothness and approximation order.