On Montel and Montel–Popoviciu Theorems in Several Variables

Authors

Asuman Güven Aksoy, Claremont McKenna CollegeFollow
Jose M. Almira, University of Jaen, Spain

Document Type

Article

Department

Mathematics (CMC)

Publication Date

10-2015

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→Rf:Rd→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.

Comments

The final published version is available in Aequationes mathematicae at Springer Link

Posted with permission.

Rights Information

© 2015 Asuman G. Aksoy, Jose M. Almira

DOI

10.1007/s00010-014-0329-8

Recommended Citation

A. G. Aksoy, J. Almira, On Montel and Montel -Popoviciu theorems in several variables, Aequationes mathematicae, 89(5), 2015 pp. 1335{1357, 2015, DOI: 10.1007/s00010-014-0329-8.