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Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 1, Pages 39–51 (Mi faa2852)  

This article is cited in 6 scientific papers (total in 7 papers)

On the Spectrum of a Vector Schrödinger Operator

R. S. Ismagilova, A. G. Kostyuchenkob

a N. E. Bauman Moscow State Technical University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We consider the asymptotics of the spectrum of a Sturm–Liouville operator acting on a space of vector functions and show that this asymptotics is affected by “rotation” of eigenvectors of the potential. A similar result is obtained for a vector Schrödinger operator.

Keywords: Schrödinger operator, self-adjointness, discrete spectrum, counting function

DOI: https://doi.org/10.4213/faa2852

Full text: PDF file (216 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2007, 41:1, 31–41

Bibliographic databases:

UDC: 517.98
Received: 19.04.2006

Citation: R. S. Ismagilov, A. G. Kostyuchenko, “On the Spectrum of a Vector Schrödinger Operator”, Funktsional. Anal. i Prilozhen., 41:1 (2007), 39–51; Funct. Anal. Appl., 41:1 (2007), 31–41

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. S. Ismagilov, A. G. Kostyuchenko, “On the Asymptotics of the Spectrum of a Nonsemibounded Vector Sturm–Liouville Operator”, Funct. Anal. Appl., 42:2 (2008), 89–97  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Ismagilov R.S., Kostyuchenko A.G., “An invariant of a pair of symmetric operators and the spectra of nonsemibounded Sturm-Liouville vector operators”, Dokl. Math., 78:3 (2008), 819–821  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    3. Ya. T. Sultanaev, O. V. Myakinova, “On the Deficiency Indices of a Singular Differential Operator of Fourth Order in the Space of Vector Functions”, Math. Notes, 86:6 (2009), 895–898  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. M. S. Agranovich, V. M. Buchstaber, R. S. Ismagilov, B. S. Kashin, B. S. Mityagin, S. P. Novikov, V. A. Sadovnichii, A. G. Sergeev, Ya. G. Sinai, A. A. Shkalikov, “Anatolii Gordeevich Kostyuchenko (obituary)”, Russian Math. Surveys, 65:4 (2010), 767–780  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Myakinova O.V., Sultanaev Ya.T., “Asymptotics of the spectrum of a singular nonsemibounded fourth-order vector differential operator in a vector function space”, Dokl. Math., 81:3 (2010), 348–350  crossref  mathscinet  zmath  isi  elib  elib
    6. N. F. Valeev, È. A. Nazirova, Ya. T. Sultanaev, “Distribution of the eigenvalues of singular differential operators in a space of vector-functions”, Trans. Moscow Math. Soc., 75 (2014), 89–102  mathnet  crossref  elib
    7. Mikhailets V., Murach A., Novikov V., “Localization Principles For Schrodinger Operator With a Singular Matrix Potential”, Methods Funct. Anal. Topol., 23:4 (2017), 367–377  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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