On Montel and Montel-Popoviciu theorems in several variables

Abstract

We present an elementary proof of a general version of Montel's theorem in several variables which is based on the use of tensor product polynomial interpolation. We also prove a Montel-Popoviciu's type theorem for functions $f:{\mathbb{R}}^d\to \mathbb{R}$ for $d>1$. Furthermore, our proof of this result is also valid for the case $d=1$, differing in several points from Popoviciu's original proof. Finally, we demonstrate that our results are optimal.

16 pages, submitted to a Journal

References in corpus (2)

• On Montel's theorem in several variables
• A qualitative description of graphs of discontinuous polynomial functions