Gaussian radial basis functions and the approximation of input-output maps

Radial basis functions are of interest in connection with a variety of approximation problems in the neural networks area, and in other areas as well. Here we show that the members of some interesting families of shift-varying input-output maps, that take a function space into a function space, can be uniformly approximated, over an infinite time or space domain, in a certain special way using Gaussian radial basis functions.