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Zap. Nauchn. Sem. POMI, 2003, Volume 295, Pages 204–243 (Mi znsl1262)  

This article is cited in 3 scientific papers (total in 3 papers)

Schrödinger operator in a periodic waveguide on the plane and quasi-conformal mappings

R. G. Shterenberg

Saint-Petersburg State University

Abstract: A magneric Schrödinger operator with variable metric in a two-dimensional simply connected periodic waveguide is considered. All coefficients are assumed to be periodic along the waveguide. We investigate Dirichlet and Neumann boundary problems as well as boundary problem of the third type. Under wide conditions on the boundary of the waveguide providing band structure of the spectrum, we prove the absolute continuity of the spectrum.

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English version:
Journal of Mathematical Sciences (New York), 2005, 127:2, 1936–1956

Bibliographic databases:

UDC: 517
Received: 10.04.2002

Citation: R. G. Shterenberg, “Schrödinger operator in a periodic waveguide on the plane and quasi-conformal mappings”, Boundary-value problems of mathematical physics and related problems of function theory. Part 33, Zap. Nauchn. Sem. POMI, 295, POMI, St. Petersburg, 2003, 204–243; J. Math. Sci. (N. Y.), 127:2 (2005), 1936–1956

Citation in format AMSBIB
\Bibitem{Sht03}
\by R.~G.~Shterenberg
\paper Schr\"odinger operator in a~periodic waveguide on the plane and quasi-conformal mappings
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 295
\pages 204--243
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1262}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1983118}
\zmath{https://zbmath.org/?q=an:1116.78013}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 127
\issue 2
\pages 1936--1956
\crossref{https://doi.org/10.1007/s10958-005-0152-9}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. G. Shterenberg, “Absolute continuity of the spectrum of two-dimensional periodic Schrödinger operators with strongly subordinate magnetic potential”, J. Math. Sci. (N. Y.), 129:4 (2005), 4087–4109  mathnet  crossref  mathscinet  zmath
    2. L. I. Danilov, “The absence of eigenvalues in the spectrum of ageneralized two-dimensional periodic Dirac operator”, St. Petersburg Math. J., 17:3 (2006), 409–433  mathnet  crossref  mathscinet  zmath
    3. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
  • Записки научных семинаров ПОМИ
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