Skip to main content
SpringerLink
Log in

Analog of the Krein Formula for Resolvents of Normal Extensions of a Prenormal Operator

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We prove a formula that relates resolvents of normal operators that are extensions of a certain prenormal operator. This formula is an analog of the Krein formula for resolvents of self-adjoint extensions of a symmetric operator. We describe properties of the defect subspaces of a prenormal operator.

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

Similar content being viewed by others

REFERENCES

  1. M. L. Horbachuk and V. I. Horbachuk, “Theory of self-adjoint extensions of symmetric operators. Entire operators and boundary-value problems,” Ukr. Mat. Zh., 46, No. 1-2, 55–62 (1994).

    Google Scholar 

  2. M. L. Horbachuk and V. I. Horbachuk, Boundary-Value Problems for Operator Differential Equations [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  3. E. A. Coddington, “Normal extension of formally normal operators,” Pacif. J. Math., 10, 1203–1209 (1960).

    Google Scholar 

  4. M. I. Vishik, “On general boundary-value problems for elliptic differential equations,” Tr. Mosk. Mat. Obshch., 1, 187–246 (1952).

    Google Scholar 

  5. V. É. Lyantse and O. G. Storozh, Methods of the Theory of Unbounded Operators [in Russian], Naukova Dumka, Kiev (1983).

    Google Scholar 

  6. A. V. Kuzhel', “An analog of Krein formula for resolvents of nonself-adjoint extensions of an Hermitian operator,” Teor. Funkts. Funkts. Anal. Prilozhen., Issue 36, 49–55 (1981).

  7. A. V. Kuzhel and S. A. Kuzhel, Regular Extensions of Hermitian Operators, VSP, Utrecht (1998).

    Google Scholar 

  8. M. E. Dudkin, “Singularly perturbed normal operators,” Ukr. Mat. Zh., 51, No. 8, 1045–1053 (1999).

    Google Scholar 

  9. V. D. Koshmanenko, Singular Bilinear Forms in Perturbation Theory for Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1993).

    Google Scholar 

  10. M. G. Krein, “Theory of self-adjoint extensions of positive Hermitian operators and its applications,” Mat. Sb., 20, No. 3, 431–490 (1947).

    Google Scholar 

  11. I. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Spaces [in Russian], Nauka, Moscow (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kiev Polytechnic Institute, Kiev

    M. E. Dudkin

Authors
  1. M. E. Dudkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dudkin, M.E. Analog of the Krein Formula for Resolvents of Normal Extensions of a Prenormal Operator. Ukrainian Mathematical Journal 54, 684–692 (2002). https://doi.org/10.1023/A:1021095613796

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021095613796

Keywords

Search

Navigation