  Which Levy processes satisfy Hunt's hypothesis (H) is a long-standing open
problem in probabilistic potential theory. The study of this problem for
one-dimensional Levy processes suggests us to consider (H) from the point of
view of the sum of Levy processes. In this paper, we present theorems and
examples on the validity of (H) for the sum of two independent Levy processes.
We also give a novel condition on the Levy measure which implies (H) for a
large class of one-dimensional Levy processes.
