On Montel's theorem in several variables

2013/10/12 by J. M. Almira, Almira, J. M., Kh. F. Abu-Helaiel +1
Mathematics · #39B22 #39B32 #46F05 #46F10 #47A15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:39B22 #msc:39B32 #msc:46F05 #msc:46F10 #msc:47A15

paper · pdf · doi:10.48550/arxiv.1310.3378

9 pages, submitted to a Journal

arxiv created 2014/01/05 · arxiv updated 2014/01/07

Abstract

Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of C(R,C) to give a new proof of classical Montel's theorem, about continuous solutions of Fréchet's functional equation Δ_h^mf=0, for real functions (and complex functions) of one real variable. In this paper we use similar ideas to prove a Montel's type theorem for the case of complex valued functions defined over the discrete group Z^d. Furthermore, we also state and demonstrate an improved version of Montel's Theorem for complex functions of several real variables and complex functions of several complex variables.

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