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The Schrödinger operator in a periodic waveguide on a plane and quasiconformal mappings. (English. Russian original) Zbl 1116.78013
J. Math. Sci., New York 127, No. 2, 1936-1956 (2005); translation from Zap. Nauchn. Semin. POMI 295, 204-243 (2003).
Summary: We consider the magnetic Schrödinger operator with a variable metric in a two-dimensional simply connected periodic waveguide. All the coefficients are assumed to be periodic along the waveguide. We investigate the Dirichlet and Neumann boundary problems, as well as the boundary problem of the third type. Under wide conditions on the boundary of the waveguide providing a band structure of the spectrum, we prove the absolute continuity of the spectrum.

MSC:
78A50 Antennas, waveguides in optics and electromagnetic theory
30C62 Quasiconformal mappings in the complex plane
35J10 Schrödinger operator, Schrödinger equation
35P05 General topics in linear spectral theory for PDEs
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