  We consider invariant hyperfunctions associated to automorphic forms on the
upper half plane. We give two interpretations of the period function of Maass
forms introduced by Lewis. The first interpretation shows that the period
function arises from the explicit description of a representative of the
hyperfunction associated to the Maass form. Under certain conditions,
automorphic forms determine cohomology classes in a cohomology group with
values in the hyperfunctions with bounded support on the line. A map from
hyperfunctions to holomorphic functions leads to a second, cohomological,
interpretation of the period function.
