On Montel and Montel-Popoviciu theorems in several variables

2014/07/02 by Asuman Güven Aksoy, Aksoy, A. G., J. M. Almira +1 · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical functions and polynomials #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1407.0532

openalex publication_date 2014/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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:ℝ^d→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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