TDI-Subspaces of C(R) and Some Density Problems from Neural Networks

dense in C(R)? Here we consider C(R) with the topology of uniform convergence on compact subsets. Lenze's interest in this question was prompted by a mathematical model from the theory of neural networks. More specifically, a type of multilayer feedforward network with a single hidden layer, see Lenze [11] and [12]. The consideration of this specific problem led us to the study of a more general question on translation and dilation invariant subspaces. In this paper we will report on some of the results, both old and new, in this area and apply them to the analysis of three different mathematical models which appear in the theory of neural networks. The present form of this paper owes much to Aharon Atzmon of Tel-Aviv University. In particular, he brought the important references Schwartz [18] and Harasymiv [6] to our attention, and also gave willingly and patiently of his time and knowledge. article no. 0042