  We give a generalization of the Beurling-Lax theorem both in the complex and
quaternionic settings. We consider in the first case functions meromorphic in
the right complex half-plane, and functions slice hypermeromorphic in the right
quaternionic half-space in the second case. In both settings we also discuss a
unified framework, which includes both the disk and the half-plane for the
complex case and the open unit ball and the half-space in the quaternionic
setting.
