Golomb and Weinberger  described a variational approach to interpolation which reduced the problem to minimizing a norm in a reproducing kernel Hilbert space generated by means of a small number of data points. Later, Duchon  defined radial basis function interpolants as functions which minimize a suitable seminorm given by a weight in spaces of… (More)
For μ≥-1/2, the authors have developed elsewhere a scheme for interpolation by Hankel translates of a basis function Φ in certain spaces of continuous functions Yn(n∈ℕ) depending on a weight w. The functions Φ and w are connected through the distributional identity t4n(hμ'Φ)(t)=1/w(t), where hμ' denotes the generalized Hankel transform of order μ. In this… (More)
We prove that, under certain mild conditions on the kernel function (or activation function), the family of radial basis function neural networks obtained by replacing the usual translation with the Delsarte one, and taking the same smoothing factor in all kernel nodes, has the universal approximation property.