A qualitative description of graphs of discontinuous polynomial functions
Classical Analysis and ODEs
2014-01-21 v3
Abstract
We prove that, if f:R^n\to R satisfies Fr\'echet's functional equation and f(x_1,...,x_n) is not an ordinary algebraic polynomial in the variables x_1,...,x_n, then f is unbounded on all non-empty open set U of R^n. Furthermore, the closure of its graph contains an unbounded open set.
Keywords
Cite
@article{arxiv.1401.3273,
title = {A qualitative description of graphs of discontinuous polynomial functions},
author = {J. M. Almira and Kh. F. Abu-Helaiel},
journal= {arXiv preprint arXiv:1401.3273},
year = {2014}
}
Comments
9 pages, submitted to a journal