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Conditions for the self-adjointness of the Schrodinger operator

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Abstract

Sufficient conditions are derived for the self-adjointness of the Schrödinger operator in the whole of space and in bounded regions, without supplementary boundary conditions and without any requirements concerning the existence of a spherically symmetric minorant of the potential satisfying the Titchmarsh-Sears conditions.

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Literature cited

  1. E. C. Titchmarsh, Eigenfunction Expansions, Vol. 2, Clarendon Press, Oxford (1946).

    Google Scholar 

  2. B. M. Levitan, “Note concerning a theorem of Titchmarsh and Sears,” Uspekhi Matem. Nauk,16, No. 4, 175–178 (1961).

    Google Scholar 

  3. R. S. Ismagilov, “Conditions for the self-adjointness of high-order differential operators,” Dokl. Akad. Nauk SSSR,142, No. 6, 1239–1242 (1962).

    Google Scholar 

  4. F. S. Rofe-Beketov, Semibounded Differential Operators, Function Theory, Functional Analysis and Applications [in Russian], No. 2, Khar'kov (1966), pp. 178–184.

    Google Scholar 

  5. M. G. Gimadislamov, “Sufficient conditions for the coincidence of minimal and maximal partial differential operators and for the discreteness of their spectra,” Matem. Zametki,4, No. 3, 301–313 (1968).

    Google Scholar 

  6. V. B. Lidskii, “The number of square-integrable solutions of a system of differential equations,” Dokl. Akad. Nauk SSSR,95, No. 2, 217–220 (1954).

    Google Scholar 

  7. I. M. Glazman, Direct Methods in Qualitative Spectral Analysis [in Russian], Moscow (1963).

  8. I. M. Gel'fand and G. E. Shilov, Some Problems in Differential Equation Theory, Generalized Functions [in Russian], Vol. 3, Moscow (1958).

  9. Yu. M. Berezanskii, Expansions in Characteristic Functions [in Russian], Kiev (1965).

  10. A. Ya. Povzner, “Expansions in characteristic functions of the operator—Δu+cu,” Matem. sb.,32, No. 1, 109–156 (1953).

    Google Scholar 

  11. E. A. Coddington and N. Levinson, The Theory of Ordinary Differential Equations [Russian translation], Moscow (1958).

  12. M. A. Naimark, Linear Differential Operators [in Russian], Moscow (1969).

  13. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations [in Russian], Moscow (1964).

  14. M. Sh. Birman and G. E. Skvortsov, “Square-summability of higher derivatives of solutions of Dirichlet's problem in a region with a piecewise-smooth boundary,” Izv. Vuzov Matem., No. 5, 12–21 (1962).

    Google Scholar 

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Authors and Affiliations

  1. Physicotechnical Institute of Low Temperatures, Academy of Sciences of the Ukrainian SSR, USSR

    F. S. Rofe-Beketov

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  1. F. S. Rofe-Beketov
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Translated from Matematicheskie Zametki, Vol. 8, No. 6, pp. 741–751, December, 1970.

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Rofe-Beketov, F.S. Conditions for the self-adjointness of the Schrodinger operator. Mathematical Notes of the Academy of Sciences of the USSR 8, 888–894 (1970). https://doi.org/10.1007/BF01673689

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  • DOI: https://doi.org/10.1007/BF01673689

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