Radial basis function neural networks of Hankel translates as universal approximators

Radial basis function neural networks (RBFNNs) of Hankel translates of order mu > -1/2 with a continuous activation function sigma for which the limit lim(z -> 0+) z(-mu-1/2)sigma(z) exists are shown to possess the universal approximation property in spaces of continuous and of p-integrable functions, 1 <= p < infinity, on (compact subsets of) [0, infinity) if, and only if, z(-mu-1/2)sigma(z) is not an even polynomial. This extends to the class of RBFNNs under consideration a result already known for RBFNNs of standard translates.