  We develop the complex scaling method for the Dirichlet Laplacian in a domain
with asymptotically cylindrical end. We define resonances as discrete
eigenvalues of non-selfadjoint operators, obtained as deformations of the
selfadjoint Dirichlet Laplacian $\Delta$ by means of the complex scaling. The
resonances are identified with the poles of the resolvent matrix elements
$((\Delta-\mu)^{-1}F, G)$ meromorphic continuation in $\mu$ across the
essential spectrum of $\Delta$, where $F$ and $G$ are elements of an explicitly
given set of partial analytic vectors. It turns out that the Dirichlet
Laplacian has no singular continuous spectrum, and its eigenvalues can
accumulate only at threshold values of the spectral parameter.
