Polynomial equations for additive functions I. The inner case

2022/11/07 by Gselmann, Eszter, Kiss, Gergely
#13N1 #16W20 #39B32 #43A45 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.03605

Abstract

The aim of this sequence of work is to investigate polynomial equations satisfied by additive functions. As a result of this, new characterization theorems for homomorphisms and derivations can be given. More exactly, in this paper the following type of equation is considered ∑_i=1ⁿf_i(x^p_i)g_i(x^q_i)= 0 (x∈ \mathbbF), where n is a positive integer, \mathbbF⊂ ℂ is a field, f_i, g_i\colon \mathbbF→ ℂ are additive functions and p_i, q_i are positive integers for all i=1, …, n.

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