I have a possibly complex valued convolution operator given by
$ \int_{\mathbb{R}}K(x-y)f(y)dy$
I know that the operator is self-adjoint if
$K(x)=\overline{K(-x)}$
holds. But are there softer conditions under which the operator is only normal? Every time I want to find conditions I only get the same as in the self-adjoint case.
Thanks for all ideas and helps.