  The paper is devoted to a model of a mesoscopic system consisting of a pair
of parallel planar waveguides separated by an infinitely thin semitransparent
boundary modeled by a transverse delta interaction. We develop the
Birman-Schwinger theory for the corresponding generalized Schroedinger
operator. The spectral properties become nontrivial if the barrier coupling is
not invariant with respect to longitudinal translations, in particular, there
are bound states if the barrier is locally more transparent in the mean and the
coupling parameter reaches the same asymptotic value in both directions along
the guide axis. We derive the weak-coupling expansion of the ground-state
eigenvalue for the cases when the perturbation is small in the supremum and the
L^1-norms. The last named result applies to the situation when the support of
the leaky part shrinks: the obtained asymptotics differs from that of a double
guide divided by a pierced Dirichlet barrier. We also derive an upper bound on
the number of bound states.
