  I associate to a global field K a Lax-Phillips scattering which has the
property of causality if and only if the Riemann Hypothesis holds for all the
abelian L-functions of K. As a Hilbert space closure problem this provides an
adelic variation on a theme initiated by Nyman and Beurling. The adelic aspects
are related to previous work by Tate, Iwasawa and Connes.
