Approximation capability to functions of several variables, nonlinear functionals and operators by radial basis function neural networks

The purpose of this paper is to explore the representation capability of radial basis function (RBF) neural networks. The main results are: (1) The necessary and sufficient condition for a function of one variable to be qualified as an activation function in an RBF network is that the function is not an even polynomial. (2) The capability of approximating nonlinear functionals and operators by RBF networks is revealed, using sample data either in the frequency domain or in the time domain.