  We link together three themes which had remained separated so far: the
Hilbert space properties of the Riemann zeros, the ``dual Poisson formula'' of
Duffin-Weinberger (also named by us co-Poisson formula), and the ``Sonine
spaces'' of entire functions defined and studied by de Branges. We determine in
which (extended) Sonine spaces the zeros define a complete, or minimal, system.
We obtain some general results dealing with the distribution of the zeros of
the de Branges Sonine entire functions. We draw attention onto some
distributions associated with the Fourier transform and which we introduced in
our earlier works.
