On polynomial functions on non-conmmutative groups

2016/12/12 by J. M. Almira, Almira, J. M., Ekaterina Shulman +1
Mathematics · #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1612.03826

openalex publication_date 2016/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a topological group. We investigate relations between two classes of "polynomial like" continuous functions on G defined, respectively, by the conditions (1) Δ_hⁿ⁺¹f=0 for every h ∈ G, and (2) Δ_h_n+1 Δ_h_n⋯ Δ_h₁f=0, for every h₁,⋯, h_n+1 ∈ G. It is shown that for many (but not all) groups these classes coincide. We consider also Montel type versions of the above conditions - when (1) and (2) hold only for steps h in a generating subset of G. Our approach is based on the study of the counterparts of the discussed classes for general representations of groups (instead of the regular representation).

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