Skip to main content
Log in

The inversion of normally solvable linear operators perturbed on the spectrum

  • Published:
Ukrainian Mathematical Journal Aims and scope

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

Access this article

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

Instant access to the full article PDF.

Literature cited

  1. M. V. Keldysh, “On eigenvalues and eigenfunctions of some classes of nonself-adjoint equations,” Dokl. Akad. Nauk SSSR,77, No. 1 (1951).

  2. M. I. Vishik and L. A. Lyusternik, “The solution of some problems on perturbations in the case of matrices and self-adjoint and nonself-adjoint differential equations,” Usp. Matem. Nauk,15, No. 3 (1960).

  3. T. Kato, Perturbation Theory of Linear Operators [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  4. M. M. Vainberg and V. A. Trenogin, The Theory of Bifurcation of Solutions of Nonlinear Equations [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  5. V. P. Trofimov, “On root subspaces of operators which depend analytically on a parameter,” Mathematical Studies,3, No. 3 (9), Kishinev (1968).

  6. T. Sabirov, “On the problem of the calculation of the nonregular part of the expansion of the resolvent in a neighborhood of the point spectrum,” Trudy NII Mathematics VGU, No. 4 (1974).

  7. T. Sabirov, “Studies in the theory of the birth of small periodic and almost periodic solutions from the equilibrium state in nonlinear systems of differential equations,” Abstract of Doctor's Dissertation [in Russian], Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev (1974).

    Google Scholar 

  8. Ya. D. Plotkin and A. F. Turbin, “Inverse linear operators perturbed in the spectrum,” Ukr. Matem. Zh.,23, No. 2 (1971).

  9. S. G. Krein, Linear Differential Equations in Banach Space [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  10. S. G. Krein, Linear Equations in Banach Space [in Russian], Nauka, Moscow (1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 27, No. 4, pp. 477–486, July–August, 1975.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Plotkin, Y.D., Turbin, A.F. The inversion of normally solvable linear operators perturbed on the spectrum. Ukr Math J 27, 385–393 (1975). https://doi.org/10.1007/BF01085584

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01085584

Keywords

Navigation