Wiener's tauberian theorems for the Fourier-Bessel transformation and uniform approximation by RBF networks of Delsarte translates

作者：Arteaga Cristian; Marrero Isabel^*

来源：Journal of Mathematical Analysis and Applications, 2015, 431(1): 482-493.

DOI：10.1016/j.jmaa.2015.05.026

• Bessel convolution
• Delsarte translation operator
• Fourier-Bessel transformation
• Radial basis function network
• Universal approximation
• Wiener tauberian theorems

We prove analogues of the Wiener and Wiener-Pitt tauberian theorems for the Delsarte translation and the Fourier-Bessel transformation. Through similar functional-analytic techniques, we give conditions on the kernel or activation function) for the family of radial basis RBF) neural networks obtained upon replacing the usual translation by the Delsarte one, with not necessarily the same smoothing factor in all kernel nodes, to have the universal approximation property in a certain space of continuous functions endowed with the uniform norm.

• 出版日期2015-11-1