Skip to main content
Log in

Sectorial extensions of a positive operator and the characteristic function

  • 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. T. Kato, Perturbation Theory for Linear Operators, Springer, New York (1966).

    Google Scholar 

  2. S. G. Krein, Linear Differential Equations in Banach Space, Am. Math. Soc., Providence (1971).

    Google Scholar 

  3. V. A. Derkach and M. M. Malamud, “Weyl's function of a Hermitian operator and its connection with the characteristic function,” Preprint No. 85-9, Donetsk. Fiz.-Tekh. Inst., Akad. Nauk Ukr. SSR (1985).

  4. V. A. Derkach and M. M. Malamud, “On the Weyl function and Hermitian operators with gaps,” Dokl. Akad. Nauk SSSR,293, No. 5, 1041–1046 (1986).

    Google Scholar 

  5. M. G. Krein, “The theory of selfadjoint extensions of semibounded operators,” Mat. Sb.,20 (62), No. 3, 431–498 (1947).

    Google Scholar 

  6. A. N. Kochubei, “Extensions of a positive definite symmetric operator,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 3, 168–171 (1979).

    Google Scholar 

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

    Google Scholar 

  8. V. A. Mikhailets, Spectra of operators and boundary value problems,” in: Spectral Analysis of Differential Operators [in Russian], Kiev (1980), pp. 106–131.

  9. M. G. Krein and I. E. Ovcharenko, “On Q-functions and sc-resolvents of nondensely defined Hermitian contractions,” Sib. Mat. Zh.,18, No. 5, 1032–1056 (1977).

    Google Scholar 

  10. T. Ando and K. Nishio, “Positive self-adjoint extensions of positive symmetric operators,” Tohoku Math. J.,22, 65–75 (1970).

    Google Scholar 

  11. A. V. Shtrus, “Characteristic functions of linear operators,” Izv. Akad. Nauk SSSR, Ser. Mat.,24, No. 1, 43–74 (1960).

    Google Scholar 

  12. M. A. Naimark, Linear Differential Operators [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  13. M. M. Malamud and é. R. Tsekanovskii, On sectorial extensions of positive operators. Makeevka (1984). [Manuscript deposited at VINITI, No. 4585.]

  14. é. R. Tsekanovskii, “The characteristic function and sectorial boundary-value problems,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 21–24 (1985).

    Google Scholar 

  15. é. R. Tsekanovskii and Yu. L. Shmul'yan, “The theory of biextensions of operators in rigged Hilbert spaces. Unbounded operator colligations and characteristic functions,” Usp. Mat. Nauk,32, No. 5, 69–124 (1977).

    Google Scholar 

  16. V. A. Derkach and é. R. Tsekanovskii, “On characteristic operator-functions of accretive operator colligations,” Dokl. Akad. Nauk Ukr. SSSR, Ser. A, No. 8, 16–19 (1981).

    Google Scholar 

  17. A. V. Shtraus, “On the extensions of a semibounded operator,” Dokl. Akad. Nauk SSSR,221, No. 3, 543–546 (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 2, pp. 151–158, February, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Derkach, V.A., Malamud, M.M. & Tsekanovskii, é.P. Sectorial extensions of a positive operator and the characteristic function. Ukr Math J 41, 136–142 (1989). https://doi.org/10.1007/BF01060376

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01060376

Keywords

Navigation