TDI-subspaces of C(ℝd) and some density problems from neural networks

Abstract

In this paper we consider translation and dilation invariant subspaces of C(ℝd). We characterize all such subspaces and also identify those f∈ C(ℝd), the span of whose translates and dilates generate non-trivial subspaces. We apply these and related results to some mathematical models in the theory of neural networks. © 1996 Academic Press, Inc.