If $E$ is a vector space, is there an established terminology for functions $f:E\times E\to\mathbb R$ whose values $f(x,y)$ only depend on $y-x$?

26 Views Asked by At

Let $E$ be a $\mathbb R$-vector space and $f:E\times E\to\mathbb R$ with $$f(x,y):=g(y-x)\;\;\;\text{for all }x,y\in E.$$

Is there an established terminology for such a function $f$?

(I'm aware of a similar terminology in the case of normed $\mathbb R$-vector spaces $X$: A function $h:X\to\mathbb R$ is called radial if $h(x)=r(\left\|x\right\|_X)$ for some $r:[0,\infty)\to\mathbb R$.)