On the Approximation Order of Principal Shift-Invariant Subspaces ofLp([formula omitted]d)

Abstract

For 1⩽p⩽∞, sufficient conditions on the generators {φh}h>0are given which ensure that theh-dilates of the shift-invariant space generated byφhprovideLp-approximation of orderk>0. Examples whereφhis an exponential box spline or certain dilates of the Gaussiane−| · |2are considered; it is shown that our sufficient condition then provides an optimal lower bound on their approximation order.