Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Some bounds at infinity for characteristic functions of the Schroedinger operator

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    Yu. M. Berezanskii, Expansions in Characteristic Functions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).

  2. 2.

    I. M. Gel'fand and G. E. Shilov, Some Problems in the Theory of Differential Equations [in Russian], Fizmatgiz, Moscow (1958).

  3. 3.

    I. M. Gel'fand and A. G. Kostyuchenko, On the Expansion in Characteristic Functions of Differential and Other Operators, Dokl. Akad. Nauk SSSR,103, No. 3, 349–352 (1955).

  4. 4.

    É. É. Shnol', Behavior of Characteristic Functions and Spectra of Sturm-Liouville Operators, Uspekh. Matem. Nauk,9, No. 4 (62), 113–132 (1954).

  5. 5.

    Yu. M. Berezanskii, On the Expansion in Characteristic Functions of Self-Adjoint Operators, Ukrainsk. Matem. Zh.,9, No. 1, 16–24 (1959).

  6. 6.

    A. G. Kostyuchenko, On the Spectral Properties of Self-Adjoint Elliptic Operators, Dokl. Akad. Nauk SSSR,115, No. 1, 34–37 (1957).

  7. 7.

    V. A. Steklov, A Method of Solving Problems of the Expansion of Functions in a Series of Chebyshev Polynomials, Izv. Ross. Akad. Nauk, 281–302, 303–326 (1921).

  8. 8.

    I. M. Glazman, Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators [in Russian], Fizmatgiz, Moscow (1963), pp. 293–297.

  9. 9.

    É. Schroedinger, Quantization as a Problem of Characteristic Values (second report), Variational Principles of Mechanics [in Russian], Fizmatgiz, Moscow (1959).

  10. 10.

    V. Maslov, Concerning the Asymptotics of Generalized Characteristic Functions of the Schroedinger Equation, Uspekh. Matem. Nauk,16, No. 4 (100), 253–254 (1961).

  11. 11.

    A. Ya. Povsner, On the Expansion of Arbitrary Functions in Terms of Characteristic Functions of the Operator —Δu+cu, Matem. Sborn.,32, No. 1, 109–156 (1953).

  12. 12.

    L. Garding, Eigenfunction Expansions Connected with Elliptic Differential Operators, 12 Skand. Mat. Kongr., 44–55, Lund (1953, 1954).

  13. 13.

    F. T. Mautner, On Eigenfunction Expansions, Proc. Nat. Acad. Sci. USA,39, No. 1, 49–53 (1953).

  14. 14.

    Yu. L. Daletskii, Continual Integrals Connected with Operator Evolutionary Equations, Uspekh. Matem. Nauk,17, No. 5 (107), 3–115 (1962).

  15. 15.

    Yu. B. Orochko, On the Powers of an Operator Arising from a Cauchy Problem for a Second Order Hyperbolic Equation, Ukrainsk. Matem. Zh.,18, No.4, 34–48 (1966).

  16. 16.

    Yu. B. Orochko, On the Behavior at Infinity of the Characteristic Functions of a Schroedinger Operator, Dokl. Akad. Nauk SSSR,163, No. 5, 1073–1076 (1965).

Download references

Author information

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 19, No. 3, pp. 39–52, May–June, 1967.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Orochko, Y.B. Some bounds at infinity for characteristic functions of the Schroedinger operator. Ukr Math J 19, 277–289 (1967).

Download citation


  • Characteristic Function
  • Schroedinger Operator