Jensen's Functional Equation on Involution-Generated Groups: A Square-Root Criterion, Rigidity Phenomena, and Obstruction Spaces

Dang Vo Phuc

Let $G$ be a group and $H$ an abelian group. We study normalized solutions $f:G\to H$ of the Jensen equation $f(xy)+f(x{y}^{-1})=2f(x)$ and its companion $f(xy)+f(x^{-1}y)=2f(y)$. Re…