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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 153, Pages 84–93 (Mi into365)  
This article is cited in 8 scientific papers (total in 8 papers)

On the Davies Formula for the Distribution of Eigenvalues of a Non-Self-Adjoint Differential Operator

Kh. K. Ishkin, A. V. Rezbayev

Bashkir State University, Ufa
Full-text PDF (208 kB) Citations (8)
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Abstract: In this paper, we analyze conditions under which the spectrum of the Sturm–Liouville operator on a certain smooth curve is localized near a countable number of rays. In the case where the potential is piecewise analytical, an asymptotic of eigenvalues is found for each series localized near the corresponding ray. The result obtained allows one to generalize the well-known formula for the asymptotic of the distribution function of the spectrum stated by Davies in the case of a finite number of localization rays.
Keywords: non-self-adjoint differential operator, spectral stability, localization of spectrum.
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 252, Issue 3, Pages 374–383
DOI: https://doi.org/10.1007/s10958-020-05166-5
Bibliographic databases:
Document Type: Article
UDC: 517.927.25
MSC: 34B24, 47A10
Language: Russian
Citation: Kh. K. Ishkin, A. V. Rezbayev, “On the Davies Formula for the Distribution of Eigenvalues of a Non-Self-Adjoint Differential Operator”, Complex analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 153, VINITI, Moscow, 2018, 84–93; J. Math. Sci. (N. Y.), 252:3 (2021), 374–383
Citation in format AMSBIB
\Bibitem{IshRez18}
\by Kh.~K.~Ishkin, A.~V.~Rezbayev
\paper On the Davies Formula for the Distribution of Eigenvalues of a Non-Self-Adjoint Differential Operator
\inbook Complex analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 153
\pages 84--93
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into365}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3903393}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 252
\issue 3
\pages 374--383
\crossref{https://doi.org/10.1007/s10958-020-05166-5}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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