Generalized small-dimension lemma and d’Alembert type functional equation on compact groups

Autor: Iz-iddine EL-Fassi, Abdellatif Chahbi
Rok vydání: 2021
Předmět:
Zdroj: Boletín de la Sociedad Matemática Mexicana. 27
ISSN: 2296-4495
1405-213X
DOI: 10.1007/s40590-021-00352-0
Popis: Let $${\mathbb {C}}$$ be the set of complex numbers and $$\sigma $$ be a continuous automorphism and $$\tau $$ be a continuous anti-automorphism such that $$\sigma ^{2}=\tau ^{2}=id.$$ The purpose of this paper is to generalize the small-dimension lemma [20, Small Dimension Lemma] and by help of it we find on any compact group G the non-zero continuous solutions $$f:G\rightarrow {\mathbb {C}}$$ of the functional equation $$\begin{aligned} f(x\sigma (y))+f(\tau (y)x)=2f(x)f(y), \ \ \ x,y \in G, \end{aligned}$$ in terms of continuous characters of G.
Databáze: OpenAIRE
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