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The behaviour of spectral functions of the string with boundary condition at a singular entrance endpoint

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References

  1. Kac, I.S., Behavior of spectral functions of differential systems with boundary conditions in a singular end-point. Doklady Akad. Nauk SSSR, 157 (1964), 34–37; English transl. in Soviet Math. Dokl., 5 (1964), 875–879.

    Google Scholar 

  2. Kac, I.S., The existence of spectral functions of generalized second-order differential systems with a boundary condition at the singular end. Mat. Sb. 68 (110) (1965), 174–227; English transl. in Amer. Mat. Soc. Transl. (2), 62 (1967), 204–262.

    Google Scholar 

  3. Kac, I.S., Krein, M.G., On the spectral functions of the string. Supplement II of the Russian translation of the book by F.V. Atkinson, Discrete and continuous boundary problem (“MIR”, Moscow, 1968), English transl. in Amer. Mat. Soc. Transl. (2) vol. 103 (1974), 19–102.

  4. Kac, I.S., Krein, M.G.,R-functions-analytic functions mapping the upper halfplane into itself. Supplement I of the same (see [3]; Kac, I.S., Krein, M.G., On the spectral functions of the string. Supplement II of the Russian translation of the book by F.V. Atkinson, Discrete and continuous boundary problem (“MIR”, Moscow, 1968), English transl. in Amer. Mat. Soc. Transl. (2) vol. 103 (1974), 19–102). English transl. in Amer. Mat. Soc. Transl. (2) vol. 103, (1974), 1–18.

  5. Levin, B.Ya., Distribution of Zeros of Entire Functions. Transl. of Monographs, no. 5, Amer. Mat. Soc., Providence, Rhode Island (1964).

    Google Scholar 

  6. Kac, I.S., Krein, M.G., Criteria for the discreteness of the spectrum of a singular string Izv. Vysš. Uč. Zaved, Matematika, no. 2 (3) (1958), 136–153 (in Russian).

    Google Scholar 

  7. Kac, I.S., On the existence of spectral functions of certain second-order singular differential systems. Doklady Akad. Nauk SSSR, 106 (1956), 15–18 (in Russian).

    Google Scholar 

  8. Kac, I.S., A remark on the article “The existence of spectral functions ...” (see [2]), Mat. Sb. 76 (118) (1968), 147–152; English transl. in Math. USSR Sbornic, 5 (1968), 141–145.

    Google Scholar 

  9. Kac, I.S., Compatibility of the coefficients of a generalized second-order linear differential equation. Matem. Sb. vol. 79 (1969), 368–380; English transl. in Math. USSR Sbornik, vol. 8 (1969), 345–356.

    Google Scholar 

  10. Kotani, S., On a generalized Sturm-Liouville operator with a singular boundary, Journal of Mathematics of Kyoto University, Vol. 15, No. 2 (1975), 423–454.

    Google Scholar 

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  1. Odessa Technological Institute for Food Industry M.V. Lomonosov, Sverdlova 112, 270039, Odessa, USSR

    I. S. Kac

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  1. I. S. Kac
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Kac, I.S. The behaviour of spectral functions of the string with boundary condition at a singular entrance endpoint. Integr equ oper theory 15, 768–783 (1992). https://doi.org/10.1007/BF01200699

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