Popov I.Yu.
On the point and continuous spectra for
coupled quantum waveguides and resonators.
(24K, LaTeX)

ABSTRACT.  A system of quantum resonators connected through small apertures
with a quantum waveguide and a system of waveguides coupled through 
small
windows are considered in the case of Dirichlet boundary condition. 
Solvable model based on the operator extension theory in 
Pontryagin space is suggested for the description of trapped 
modes imbedded in the continuous spectrum for the systems.
The model allows one not only to prove the existence of such modes
but also to suggest an effective and simple algorithm for its 
determination. A system of quantum waveguides coupled laterally
through small windows is considered. The existence of eigenvalue
imbedded in the continuous spectrum is shown. The case of
periodic set of windows is studied in the framework of the model. 
The dispersion equation
is obtained in an explicit form. The existence of bands imbedded in
the continuous spectrum is proved, and an algorithm for its
determination is described.