Differentiable approximation by means of the Radon transformation and its applications to neural networks (Q1891035)

This paper treats the problem of simultaneously approximating a differential function in several variables and its derivatives by superposition of a function in one variable. The usefulness of the inverse Radon transform for differentiable approximation both on compact sets and on the whole Euclidean space is shown. The presented method can be regarded as an extended alternative method of the proofs of the respective previous theorems. The proofs are constructive, except for the proof of existence of the so called delta sequences. As a neural network can output a superposition of a function, the results extend well-known neural approximation theorems which are useful in neural computation theory.