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Mat. Sb., 1998, Volume 189, Number 1, Pages 133–148 (Mi msb298)  

This article is cited in 10 scientific papers (total in 10 papers)

A class of Sturm–Liouville operators and approximate calculation of the first eigenvalues

V. A. Sadovnichii, V. E. Podolskii

M. V. Lomonosov Moscow State University

Abstract: A special class $S$ of Sturm–Liouville operators with simple asymptotic properties of eigenfunctions is investigated. The analytic properties of the potentials are analyzed and the operators in this class are described in terms of the transition function of the inverse problem. The following result is established: the class $S$ is dense in the set of Sturm–Liouville operators with potentials in $L_2$. A subset of $S$ that also has the density property is effectively distinguished. Based on the properties of the operators in this subset, a method of the approximate evaluation of the first eigenvalues of a Sturm–Liouville operator through its regularized traces is proposed and substantiated.

DOI: https://doi.org/10.4213/sm298

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English version:
Sbornik: Mathematics, 1998, 189:1, 129–145

Bibliographic databases:

UDC: 517.94
MSC: 34B24, 34L15
Received: 16.04.1997

Citation: V. A. Sadovnichii, V. E. Podolskii, “A class of Sturm–Liouville operators and approximate calculation of the first eigenvalues”, Mat. Sb., 189:1 (1998), 133–148; Sb. Math., 189:1 (1998), 129–145

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. Sadovnichii V.A., Dubrovskii V.V., Maleko E.M., “Ob odnom sposobe priblizhennogo nakhozhdeniya sobstvennykh chisel operatora Shturma-Liuvillya”, Dokl. RAN, 369:1 (1999), 16–18  mathnet  mathscinet  zmath  isi
    2. Sadovnichii, VA, “An estimate for the best approximation of solutions of the Sturm-Liouville problem with an analytic potential by partial sums of asymptotic series”, Differential Equations, 35:4 (1999), 498  mathnet  mathscinet  zmath  isi
    3. Sadovnichii, VA, “Estimates for the coefficients of asymptotic series for the solutions of the Sturm-Liouville equation with an analytic potential. I”, Differential Equations, 35:2 (1999), 284  mathnet  mathscinet  isi
    4. Sadovnichii, AVA, “Nonuniqueness of solutions to the regularized trace system”, Doklady Mathematics, 71:3 (2005), 411  zmath  isi  elib
    5. V. A. Sadovnichii, V. E. Podolskii, “Traces of operators”, Russian Math. Surveys, 61:5 (2006), 885–953  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Sadovnichii V.A.. Podol'skii V.E., “Traces of differential operators”, Differ. Equ., 45:4 (2009), 477–493  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. Aslanova N.M., “Study of the asymptotic eigenvalue distribution and trace formula of a second order operator-differential equation”, Bound Value Probl, 2011, 7  crossref  mathscinet  zmath  isi
    8. Maleko E.M., “O metode sledov rezolvent, vychislennykh tochno”, Vestnik Samarskogo gosudarstvennogo universiteta, 2011, no. 86, 37–52  mathnet  elib
    9. M. K. Kerimov, “Approximate computation of eigenvalues and eigenfunctions of Sturm–Liouville differential operators by applying the theory of regularized traces”, Comput. Math. Math. Phys., 52:3 (2012), 351–386  mathnet  crossref  zmath  adsnasa  isi  elib  elib
    10. Intissar A., “Regularized Trace Formula of Magic Gribov Operator on Bargmann Space”, J. Math. Anal. Appl., 437:1 (2016), 59–70  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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