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arXiv · 1407.0532

On Montel and Montel-Popoviciu theorems in several variables

A. G. Aksoy·J. M. Almira
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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.

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A. G. Aksoy, J. M. Almira. 2014-07-02. On Montel and Montel-Popoviciu theorems in several variables. https://arxiv.org/abs/1407.0532

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