  Partial actions of discrete abelian groups can be used to construct both
groupoid C*-algebras and partial crossed product algebras. In each case there
is a natural notion of an analytic subalgebra. We show that for countable
subgroups of the real numbers and free partial actions, these constructions
yield the same C*-algebras and the same analytic subalgebras. We also show that
under suitable hypotheses an analytic partial crossed product preserves all the
information in the dynamical system in the sense that two analytic partial
crossed products are isomorphic as Banach algebras if, and only if, the partial
actions are conjugate.
