A qualitative description of graphs of discontinuous polynomial functions

Abstract

We prove that, if f:R^n\to R satisfies Fréchet'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.

9 pages, submitted to a journal

References in corpus (1)

• On Montel's theorem in several variables

Cited by in corpus (2)

• Los teoremas de Fréchet, Montel y Popoviciu y los grafos de los polinomios discontinuos
• On Montel and Montel-Popoviciu theorems in several variables