APPROXIMATION IN Lp(Rd) FROM SPACES SPANNED BY THE PERTURBED INTEGER TRANSLATES OF A RADIAL FUNCTION

The problem of approximating smooth L p-functions from spaces spanned by the integer translates of a radially symmetric function is very well understood. In case the points of translation, , are scattered throughout R d , the approximation problem is only well understood in the \stationary" setting. In this work, we provide lower bounds on the obtainable approximation orders in the \non-stationary" setting under the assumption that is a small perturbation of Z d. The functions which we can approximate belong to certain Besov spaces. Our results, which are similar in many respects to the known results for the case = Z d , apply speciically to the examples of the Gauss kernel and the Generalized Multiquadric.