Skip to main content
SpringerLink
Log in

Spaces of boundary values and regular extensions of Hermitian operators

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

The concept of space of boundary values (SBV) is extended to the case of Hermitian, non-densely defined operators with distinct defect numbers. The properties of such SBV are investigated. The obtained results are applied to the investigation of regular (in particular, dissipative) extensions of Hermitian operators of the indicated form.

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. M. O. Talyush, “The typical structure of dissipative operators,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 11, 993–996 (1973).

    Google Scholar 

  2. A. N. Kochubei, “On the extensions of symmetric operators and symmetric binary relations,” Mat. Zametki,17, No. 1, 41–48 (1975).

    Google Scholar 

  3. V. M. Bruk, “On a certain class of boundary value problems with a spectral parameter in the boundary condition,” Mat. Sb.,100, No. 2, 200–216 (1976).

    Google Scholar 

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

    Google Scholar 

  5. O. G. Storozh, “On the extensions of symmetric operators with distinct deficiency numbers,” Mat. Zametki,36, No. 5, 791–796 (1984).

    Google Scholar 

  6. A. V. Kuzhel', The Extension of Hermitian Operators [in Russian], Vishcha Shkola, Kiev (1989).

    Google Scholar 

  7. T. Ya. Azizov and I. S. Iokhvidov, Linear Operators in Spaces with an Indefinite Metric, Wiley-Interscience, Chichester, Great Britain (1989).

    Google Scholar 

  8. A. V. Shtraus, “On extensions and the characteristic function of a symmetric operator,” Izv. Akad. Nauk SSSR, Ser. Mat.,32, No. 1, 186–207 (1968).

    Google Scholar 

  9. A. N. Kochubei, “Symmetric operators and nonclassical spectral problems,” Mat. Zametki,25, No. 3, 425–434 (1979).

    Google Scholar 

  10. A. V. Shtraus, “Generalized resolvents of symmetric operators,” Izv. Akad. Nauk SSSR, Ser. Mat.,18, No. 1, 51–86 (1954).

    Google Scholar 

  11. A. N. Kochubei, “On characteristic functions of symmetric operators and their extensions,” Izv. Akad. Nauk ArmSSR, Ser. Mat.,15, No. 3, 219–232 (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kiev University, USSR

    S. A. Kuzhel'

Authors
  1. S. A. Kuzhel'
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 854–858, June, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuzhel', S.A. Spaces of boundary values and regular extensions of Hermitian operators. Ukr Math J 42, 755–758 (1990). https://doi.org/10.1007/BF01058930

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01058930

Keywords

Search

Navigation