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Izv. IMI UdGU, 2013, Issue 1(41), Pages 78–95 (Mi iimi249)  

This article is cited in 1 scientific paper (total in 1 paper)

On the spectrum of a two-dimensional generalized periodic Schrödinger operator

L. I. Danilov

Physical Technical Institute, Ural Branch of the Russian Academy of Sciences, ul. Kirova, 132, Izhevsk, 426000, Russia

Abstract: Absolute continuity of the spectrum of a two-dimensional generalized periodic Schrödinger operator with continuous metric $g$ and scalar potential $V$ is proved provided that the Fourier coefficients of the functions $g^{\pm 1/2}$ satisfy the condition $\sum |N|^{1/2}|(g^{\pm 1/2})_N|<+\infty $ and the scalar potential $V$ has relative bound zero with respect to the operator $-\Delta $ in the sense of quadratic forms.

Keywords: generalized Schrödinger operator, absolute continuity of the spectrum, periodic potential.

Full text: PDF file (280 kB)
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UDC: 517.958+517.984.5
MSC: 35P05
Received: 15.01.2013

Citation: L. I. Danilov, “On the spectrum of a two-dimensional generalized periodic Schrödinger operator”, Izv. IMI UdGU, 2013, no. 1(41), 78–95

Citation in format AMSBIB
\Bibitem{Dan13}
\by L.~I.~Danilov
\paper On the spectrum of a two-dimensional generalized periodic Schr\"odinger operator
\jour Izv. IMI UdGU
\yr 2013
\issue 1(41)
\pages 78--95
\mathnet{http://mi.mathnet.ru/iimi249}


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    This publication is cited in the following articles:
    1. L. I. Danilov, “O spektre dvumernogo obobschennogo periodicheskogo operatora Shredingera. II”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 3–28  mathnet
  • Известия Института математики и информатики Удмуртского государственного университета
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