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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 2, Pages 27–37 (Mi faa3107)  

This article is cited in 2 scientific papers (total in 2 papers)

Absence of Eigenvalues for the Periodic Schrödinger Operator with Singular Potential in a Rectangular Cylinder

I. Kachkovskii

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We consider the periodic Schrödinger operator on a $d$-dimensional cylinder with rectangular section. The electric potential may contain a singular component of the form $\sigma(x,y)\delta_{\Sigma}(x,y)$, where $\Sigma$ is a periodic system of hypersurfaces. We establish that there are no eigenvalues in the spectrum of this operator, provided that $\Sigma$ is sufficiently smooth and $\sigma\in L_{p,\operatorname{loc}}(\Sigma)$, $p>d-1$.

Keywords: Schrödinger operator, periodic coefficients, absolutely continuous spectrum

DOI: https://doi.org/10.4213/faa3107

Full text: PDF file (194 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:2, 104–112

Bibliographic databases:

UDC: 517.984.56
Received: 05.12.2012

Citation: I. Kachkovskii, “Absence of Eigenvalues for the Periodic Schrödinger Operator with Singular Potential in a Rectangular Cylinder”, Funktsional. Anal. i Prilozhen., 47:2 (2013), 27–37; Funct. Anal. Appl., 47:2 (2013), 104–112

Citation in format AMSBIB
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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. A. O. Prokhorov, N. D. Filonov, “The Maxwell operator with periodic coefficients in a cylinder”, St. Petersburg Math. J., 29:6 (2018), 997–1006  mathnet  crossref  mathscinet  isi  elib
    2. I. V. Kachkovskii, N. D. Filonov, “Absolyutnaya nepreryvnost spektra periodicheskogo operatora Shredingera v tsilindre s tretim kraevym usloviem”, Funkts. analiz i ego pril., 54:2 (2020), 48–57  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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