Radial basis function neural networks of Hankel translates as universal approximators

Abstract

Radial basis function neural networks (RBFNNs) of Hankel translates of order [Formula: see text] with a continuous activation function [Formula: see text] for which the limit [Formula: see text] exists are shown to possess the universal approximation property in spaces of continuous and of [Formula: see text]-integrable functions, [Formula: see text], on (compact subsets of) [Formula: see text] if, and only if, [Formula: see text] is not an even polynomial. This extends to the class of RBFNNs under consideration a result already known for RBFNNs of standard translates.