Solving Universal Approximation Problem by Hankel Approximate Identity Neural Networks in Function Spaces

Abstract

Artificial neural networks has been effectively applied to numerous applications because of their universal approximation property. This work is grounded on two frameworks. Firstly, it is concerned with solving universal approximation problem by a class of neural networks based on Hankel approximate identity which is embedded in the space of continuous functions on real positive numbers. Secondly, this problem solving will be investigated in the Lebesgue spaces on real positive numbers. The methods are constructed on the notions of Hankel convolution linear operators, Hankel approximate identity, and epsilon-net.