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Asymptotic formulas for the eigenvalues of the Sturm-Liouville operator

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Literature Cited

  1. C. Clark, “The asymptotic distribution of eigenvalues and eigenfunctions for elliptic boundary-value problems,” SIAM Rev.,9, No. 4, 627–646 (1967).

    Google Scholar 

  2. M. Sh. Birman and M. Z. Solomyak, “The asymptotics of the spectrum of a differential equation,” in: Results of Science and Technology, Series: Mathematical Analysis [in Russian], Vol. 14, Nauka, Moscow (1977), pp. 5–58.

    Google Scholar 

  3. A. G. Kostyuchenko and I. S. Sargsyan, Distribution of Eigenvalues [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  4. K. Kh. Boimatov, “Distribution of eigenvalues of degenerate elliptic operators,” Dokl. Akad. Nauk SSSR,248, No. 3, 521–524 (1979).

    Google Scholar 

  5. M. Otelbaev, “On Titchmarsh' method of estimating the resolvent,” Dokl. Akad. Nauk SSSR,211, No. 4, 787–790 (1973).

    Google Scholar 

  6. K. Kh. Boimatov, “Asymptotics of the Schrödinger spectrum,” Diff. Uravn.,10, No. 11, 1939–1945 (1974).

    Google Scholar 

  7. K. Kh. Boimatov, “Asymptotics of the spectrum of the Schrödinger operator with a singular potential,” Usp. Mat. Nauk,31, No. 1, 241–242 (1976).

    Google Scholar 

  8. G. V. Rozenblyum, “Distribution of the discrete spectrum of a singular differential operator,” Dokl. Akad. Nauk SSSR,202, No. 5, 1012–1015 (1972).

    Google Scholar 

  9. M. Otelbaev and Kh. T. Sultanaev, “On formulas for the distribution of eigenvalues of singular differential operators,” Mat. Zametki,14, No. 3, 361–368 (1973).

    Google Scholar 

  10. O. D. Apyshev and M. Otelbaev, “On the classical formula for the distribution of eigehvalues of the Sturm-Liouville operator,” Izv. Akad. Nauk KazSSR, Ser. Fiz.-Mat., No. 3, 24–28 (1975).

    Google Scholar 

  11. M. Otelbaev, “Asymptotics of eigenvalues of the Sturm-Liouville operator. 1,” Izv. Akad. Nauk KazSSR, Ser. Fiz.-Mat., No. 5, 40–44 (1979).

    Google Scholar 

  12. O. D. Apyshev, “On the spectrum of elliptic equations,” Doctoral Thesis, Institute of Mathematics and Mechanics, Academy of Sciences of the Kazakh SSR, Alma-Ata (1978).

    Google Scholar 

  13. N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, Ungar Press.

  14. M. Otelbaev, “Asymptotics of eigenvalues of the Sturm-Liouville operator. 2,” Izv. Akad Nauk KazSSR, Ser. Fiz.-Mat., No. 1, 48–52 (1980).

    Google Scholar 

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Institute of Mathematics, Academy of Sciences of the Kazakh SSR, Alma-Ata. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 24, No. 4, pp. 116–130, July–August, 1983.

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Otelbaev, M. Asymptotic formulas for the eigenvalues of the Sturm-Liouville operator. Sib Math J 24, 586–598 (1983). https://doi.org/10.1007/BF00969556

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