A note on the problem of straight-line interpolation by ridge functions
Classical Analysis and ODEs
2025-12-05 v2
Abstract
In this paper we discuss the problem of interpolation on straight lines by linear combinations of ridge functions with fixed directions. By using some geometry and/or systems of linear equations, we constructively prove that it is impossible to interpolate arbitrary data on any three or more straight lines by sums of ridge functions with two fixed directions. The general case with more straight lines and more directions is reduced to the problem of existence of certain sets in the union of these lines.
Cite
@article{arxiv.2408.06443,
title = {A note on the problem of straight-line interpolation by ridge functions},
author = {Azer Akhmedov and Vugar Ismailov},
journal= {arXiv preprint arXiv:2408.06443},
year = {2025}
}
Comments
10 pages, minor corrections; to appear in Real Analysis Exchange