**
Below is the ascii version of the abstract for 03-525.
The html version should be ready soon.**D. Borisov and P. Exner
Exponential splitting of bound states in
a waveguide with a pair of distant windows
(102K, LaTeX2e, 1 ps-figure)
ABSTRACT. We consider Laplacian in a straight planar strip with
Dirichlet boundary which has two Neumann ``windows'' of the same
length the centers of which are $2l$ apart, and study the
asymptotic behaviour of the discrete spectrum as $l\to\infty$. It
is shown that there are pairs of eigenvalues around each isolated
eigenvalue of a single-window strip and their distances vanish
exponentially in the limit $l\to\infty$. We derive an asymptotic
expansion also in the case where a single window gives rise to a
threshold resonance which the presence of the other window turns
into a single isolated eigenvalue.