Properties of d'Alembert functions

Henrik Stetkær

Properties of d'Alembert functions

Research output: Working paper/Preprint › Working paper › Research

Abstract

We study properties of solutions $f$ of d'Alembert's functional equations on a topological group $G$ . For nilpotent groups and for connected, solvable Lie groups $G$ , we prove that $f$ has the form $f(x) = (\gamma(x) + \gamma (x^{-1}))/2$ , $x \in G$ , where $\gamma$ is a continuous homomorphism of $G$ into the multiplicative group $\mathbb{C}\setminus \{ 0\}$ . We give conditions on $G$ and/or $f$ for equality in the inclusion $\{ u \in G \mid f(xu) = f(x)$ for all $x \in G\} \subseteq \{u \in G \mid f(u) =1\}$ .

Original language	English
Place of publication	Århus
Publisher	Department of Mathematical Sciences , University of Aarhus
Number of pages	22
Publication status	Published - 2007

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author = "Henrik Stetk{\ae}r",

year = "2007",

language = "English",

publisher = "Department of Mathematical Sciences , University of Aarhus",

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M3 - Working paper

BT - Properties of d'Alembert functions

PB - Department of Mathematical Sciences , University of Aarhus

CY - Århus

ER -

Properties of d'Alembert functions

Abstract

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