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On Montel and Montel–Popoviciu theorems in several variables

Aequationes mathematicae volume 89, pages 1335–1357 (2015)Cite this article

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 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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Authors and Affiliations

  1. Department of Mathematics, Claremont McKenna College, Claremont, CA, 91711, USA

    A. G. Aksoy

  2. Departamento de Matemáticas, E.P.S. Linares, Universidad de Jaén, C/ Alfonso X el Sabio, 28, 23700, Linares (Jaén), Spain

    J. M. Almira

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  1. A. G. Aksoy
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  2. J. M. Almira
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Aksoy, A.G., Almira, J.M. On Montel and Montel–Popoviciu theorems in several variables. Aequat. Math. 89, 1335–1357 (2015). https://doi.org/10.1007/s00010-014-0329-8

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  • DOI: https://doi.org/10.1007/s00010-014-0329-8

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