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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 4(8), Pages 474–503 (Mi msb3269)  

This article is cited in 4 scientific papers (total in 4 papers)

Defect indices of $J_m$-matrices and of differential operators with polynomial coefficients

A. L. Chistyakov


Abstract: The problem of the defect indices of the symmetric operator $C$ which acts on the space $l_2$ and is generated by a regular Hermitian $J_m$-matrix with increasing elements is investigated. The asymptotics, as $k\to\infty$, of the eigenvectors $U=(u_0,u_1,…,u_k,…)$ of the operator $C^*$ which correspond to the nonreal eigenvalues are obtained. The results are applied to ordinary differential operators with polynomial coefficients defined on the entire $x$-axis.
Figures: 2.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:4, 471–500

Bibliographic databases:

UDC: 517.948+513.88
MSC: Primary 47B25, 47E05; Secondary 15A21
Received: 16.04.1970

Citation: A. L. Chistyakov, “Defect indices of $J_m$-matrices and of differential operators with polynomial coefficients”, Mat. Sb. (N.S.), 85(127):4(8) (1971), 474–503; Math. USSR-Sb., 14:4 (1971), 471–500

Citation in format AMSBIB
\Bibitem{Chi71}
\by A.~L.~Chistyakov
\paper Defect indices of $J_m$-matrices and of differential operators with polynomial coefficients
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 4(8)
\pages 474--503
\mathnet{http://mi.mathnet.ru/msb3269}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=284861}
\zmath{https://zbmath.org/?q=an:0225.47017}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 4
\pages 471--500
\crossref{https://doi.org/10.1070/SM1971v014n04ABEH002816}


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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. A. G. Kostyuchenko, K. A. Mirzoev, “Generalized Jacobi Matrices and Deficiency Numbers of Ordinary Differential Operators with Polynomial Coefficients”, Funct. Anal. Appl., 33:1 (1999), 25–37  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Nagy B., “Multiplicities, Generalized Jacobi Matrices, and Symmetric Operators”, Journal of Operator Theory, 65:1 (2011), 211–232  mathscinet  zmath  isi
    3. K. A. Mirzoev, N. N. Konechnaya, T. A. Safonova, R. N. Tagirova, “Obobschennye yakobievy matritsy i spektralnyi analiz differentsialnykh operatorov s polinomialnymi koeffitsientami”, Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 152, VINITI RAN, M., 2018, 91–102  mathnet  mathscinet
    4. I. N. Braeutigam, D. M. Polyakov, “Asymptotics of eigenvalues of infinite block matrices”, Ufa Math. J., 11:3 (2019), 11–28  mathnet  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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