Description of low-frequency parts of the spectrum of periodical waveguide with screens

We study the motion of waves or quantum particles through a periodical waveguide with screens. We start with one screen and progress to periodical case. In a stripe /spl Omega/=(R/spl bsol/{0})/spl times/[0,/spl pi/]/spl I.such/(x, y) we consider Laplacian with Dirichlet boundary conditions on upper y=/spl pi/ and lower y=0 lines, and with perturbation on a segment {0}/spl times/[0,/spl pi/]. We study the self-adjoint case.