TDI-Subspaces ofC(Rd) and Some Density Problems from Neural Networks Original Research Article

In this paper we consider translation and dilation invariant subspaces ofC(Rd). We characterize all such subspaces and also identify thosef∈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.