  The weighted shift operators turn out to be extremely useful in supplying
interesting examples of operators on Hilbert spaces. With a view to study a
continuous analogue of weighted shifts, M. Embry and A. Lambert initiated the
study of a semigroup of operators $\{S_t\}$ indexed by a non-negative real
number $t$ and termed it as weighted translation semigroup. The operators $S_t$
are defined on $L^2(\mathbb R_+)$ by using a weight function. In this paper, we
continue the work carried out there and obtain characterizations of
hyperexpansive weighted translation semigroups in terms of their symbols. We
also discuss Cauchy dual of a hyperexpansive weighted translation semigroup. As
an application of the techniques developed, we present new proofs of a couple
of known results.
