Skip to main content
SpringerLink
Log in

Some properties of the expansions relative to the generalized eigenfunctions of carleman self-adjoint operators

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. I. M. Glazman, Direct Methods of the Qualitative Spectral Analysis of Singular Differential Operators [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

  2. I. M. Gel'fand and A. G. Kostyuchenko, “On expansions in eigenfunctions of differential and other operators,” Dokl. Akad. Nauk SSR,103, No. 3, 349–352 (1955).

    Google Scholar 

  3. Yu. M. Berezanskii (Ju. M. Berezanskii), Expansions in Eigenfunctions of Self-Adjoint Operators, Amer. Math. Soc., Providence (1968).

    Google Scholar 

  4. K. Maurin, Methods of Hilbert Spaces, Polish Scientific Publishers, Warszawa (1972).

    Google Scholar 

  5. Yu. B. Orochko, “On the theory of expansions in generalized eigenfunctions of self-adjoint operators,” Ukr. Mat. Zh.,30, No. 1, 63–69 (1978).

    Google Scholar 

  6. Yu. B. Orochko, “Certain estimates at infinity for the eigenfunctions of the Schrödinger operator,” Ukr. Mat. Zh.,19, No. 3, 39–53 (1967).

    Google Scholar 

  7. A. G. Geidarov, “The eigenfunction expansion of self-adjoint elliptic operators with a singular potential,” in: Proceedings of an All-Union Conference on Partial Differential Equations dedicated to Acad. I. G. Petrovskii on the occasion of his 75th birthday, Moscow University, Moscow (1978), pp. 287–288.

  8. Yu. B. Orochko, “A hyperbolic equation method in the spectral theory of the Schrödinger operator with a real singular potential,” in: Proceedings of an All-Union Conference on Partial Differential Equations dedicated to Acad. I. G. Petrovskii on the occasion of his 75th birthday, Moscow University, Moscow (1978), pp. 403–404.

  9. V. F. Kovalenko and Yu. A. Semenov, “Some problems of the expansions in generalized eigenfunctions of of the Schrödinger operator with strongly singular potentials,” Usp. Mat. Nauk,33, No. 4, 107–140 (1978).

    Google Scholar 

  10. G. I. Kats, “Spectral expansions of self-adjoint operators in generalized eigenelements of a Hilbert space,” Ukr. Mat. Zh.,13, 13–33 (1961).

    Google Scholar 

  11. G. I. Kats, “Generalized elements of Hilbert spaces,” Ukr. Mat. Zh.,12, No. 1, 13–24 (1960).

    Google Scholar 

  12. N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space, Ungar, New York (1961).

    Google Scholar 

  13. Yu. M. Berezanskii, “On the expansions in eigenfunctions of self-adjoint operators,” Ukr. Mat. Zh.,11, No. 1, 16–24 (1959).

    Google Scholar 

  14. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness, Academic Press, New York (1979).

    Google Scholar 

Download references

Authors
  1. Yu. B. Orochko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Moscow Institute of Electronic Machine Construction. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 21, No. 6, pp. 96–107, November–December, 1980.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Orochko, Y.B. Some properties of the expansions relative to the generalized eigenfunctions of carleman self-adjoint operators. Sib Math J 21, 824–833 (1980). https://doi.org/10.1007/BF00968469

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00968469

Keywords

Search

Navigation