Radial tempered distribution
= Radial tempered distribution
For $n>1$, a <tempered distribution> $T$ on $\mathbb R^n$ is radial when $T\circ R=T$ for every $R\in SO(n)$, where $\langle T\circ R,\varphi\rangle=\langle T,\varphi\circ R^t\rangle$. This agrees with the usual <radial function> definition for regular smooth distributions, because the <special orthogonal group> acts transitively on spheres.