  We show that a combination of well-known operators, namely
$\I{\tau}\circ{H}\circ\Ps$ is self-adjoint and {\em ad-hoc} related to the
$\zeta$ function. Here ${\tau}$ is an involution appearing in Weil's positivity
criteria needed for hermitrization, $H$ a regularization operator introduced by
Connes \cite{Co2} and $\Ps$ essentially Poisson summation. We elaborate on the
Hilbert-P\'olya conjecture, discuss why the Hermite-Biehler theorem,
uncertainty relations and cohomologies are interesting in our scenario.
