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Funktsional'nyi Analiz i ego Prilozheniya, 2010, Volume 44, Issue 2, Pages 87–91
DOI: https://doi.org/10.4213/faa2982
(Mi faa2982)
 

This article is cited in 33 scientific papers (total in 33 papers)

Brief communications

One-dimensional Schrödinger operator with $\delta$-interactions

A. S. Kostenkoa, M. M. Malamudb

a School of Mathematical Sciences, Dublin Institute of Technology
b Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, Donetsk
References:
Abstract: The one-dimensional Schrödinger operator $\mathrm{H}_{X,\alpha}$ with $\delta$-interactions on a discrete set is studied in the framework of the extension theory. Applying the technique of boundary triplets and the corresponding Weyl functions, we establish a connection of these operators with a certain class of Jacobi matrices. The discovered connection enables us to obtain conditions for the self-adjointness, lower semiboundedness, discreteness of the spectrum, and discreteness of the negative part of the spectrum of the operator $\mathrm{H}_{X,\alpha}$.
Keywords: Schrödinger operator, point interactions, self-adjointness, lower semiboundedness, discreteness.
Received: 08.07.2009
English version:
Functional Analysis and Its Applications, 2010, Volume 44, Issue 2
DOI: https://doi.org/10.1007/s10688-010-0019-9
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: A. S. Kostenko, M. M. Malamud, “One-dimensional Schrödinger operator with $\delta$-interactions”, Funktsional. Anal. i Prilozhen., 44:2 (2010), 87–91
Citation in format AMSBIB
\Bibitem{KosMal10}
\by A.~S.~Kostenko, M.~M.~Malamud
\paper One-dimensional Schr\"odinger operator with $\delta$-interactions
\jour Funktsional. Anal. i Prilozhen.
\yr 2010
\vol 44
\issue 2
\pages 87--91
\mathnet{http://mi.mathnet.ru/faa2982}
\crossref{https://doi.org/10.4213/faa2982}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2681961}
\zmath{https://zbmath.org/?q=an:1210.47068}
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  • https://www.mathnet.ru/eng/faa/v44/i2/p87
  • This publication is cited in the following 33 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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