The universal approximation capabilities of double 2 pi-periodic approximate identity neural networks

摘要

The purpose of this study is to investigate the universal approximation capabilities of a certain class of single-hidden-layer feedforward neural networks, which is called double 2 pi-periodic approximate identity neural networks. Using double 2 pi-periodic approximate identity, several theorems concerning the universal approximation capabilities of the networks are proved. The proofs of these theorems are sketched based on the double convolution linear operators and the definition of is an element of-net. The obtained results are divided into two categories. First, the universal approximation capability of the networks is shown in the space of continuous bivariate 2 pi-periodic functions. Then, universal approximation capability of the networks is extended to the space of pth-order Lebesgue-integrable bivariate 2 pi-periodic functions. These results can be interpreted as an extension of the universal approximation capabilities established for single-hidden-layer feedforward neural networks.