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Mat. Zametki, 1971, Volume 9, Issue 4, Pages 401–408 (Mi mz7022)  

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

Discreteness of the spectrum and completeness of systems of characteristic and associated vectors of second-order nonself-adjoint differential operators

I. I. Golichev

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: Conditions are found under which $A^1\in\sigma_p$ ($A$ is a nonself-adjoint operator). For differential operators in $L_2(-\infty, \infty)$ with real coefficients, conditions are found for the existence of a regular point, necessary and sufficient and also sufficient conditions are found for the spectrum to be discrete, and conditions are found for the system of characteristic and associated vectors to be complete.

Full text: PDF file (484 kB)

English version:
Mathematical Notes, 1971, 9:4, 230–234

Bibliographic databases:

UDC: 513.88
Received: 17.02.1970

Citation: I. I. Golichev, “Discreteness of the spectrum and completeness of systems of characteristic and associated vectors of second-order nonself-adjoint differential operators”, Mat. Zametki, 9:4 (1971), 401–408; Math. Notes, 9:4 (1971), 230–234

Citation in format AMSBIB
\Bibitem{Gol71}
\by I.~I.~Golichev
\paper Discreteness of the spectrum and completeness of systems of characteristic and associated vectors of second-order nonself-adjoint differential operators
\jour Mat. Zametki
\yr 1971
\vol 9
\issue 4
\pages 401--408
\mathnet{http://mi.mathnet.ru/mz7022}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=284862}
\zmath{https://zbmath.org/?q=an:0226.47022|0216.16402}
\transl
\jour Math. Notes
\yr 1971
\vol 9
\issue 4
\pages 230--234
\crossref{https://doi.org/10.1007/BF01387770}


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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. I. I. Golichev, P. E. Krasnushkin, “Spectral-source-like expansions in the theory of wave propagation and the quantum theory of potential scattering”, Theoret. and Math. Phys., 10:3 (1972), 250–263  mathnet  crossref  mathscinet
  • Математические заметки Mathematical Notes
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