On the representation by bivariate ridge functions
Classical Analysis and ODEs
2016-06-28 v1 Analysis of PDEs
Abstract
We consider the problem of representation of a bivariate function by sums of ridge functions. We show that if a function of a certain smoothness class is represented by a sum of finitely many, arbitrarily behaved ridge functions, then it can also be represented by a sum of ridge functions of the same smoothness class. As an example, this result is applied to a homogeneous constant coefficient partial differential equation.
Cite
@article{arxiv.1606.07940,
title = {On the representation by bivariate ridge functions},
author = {Rashid Aliev and Vugar Ismailov},
journal= {arXiv preprint arXiv:1606.07940},
year = {2016}
}
Comments
8 pages