In his 1970 paper, on page 124, Hormander discusses fundamental solutions of linear PDE with constant coefficients. I notice he only discusses cases where the support $F$ of the fundamental solution is either a half-space or contained in a proper cone. Are there known constant-coefficient PDE's whose fundamental solution has a support $F$ which is not contained in a proper cone nor does it fill up a half-space (Say, there exists a plane $H$ where for every point $x \in H_0$ there is an open ball $B_x$ centered on $x$ so that $F\cap B_x = \emptyset$).
I'm not an expert in the subject, so I apologize beforehand if the question is too standard.
