Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Positive spaces of boundary values and sectorial extensions of a nonnegative symmetric operator

  • 24 Accesses

  • 5 Citations

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

Literature cited

  1. 1.

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

  2. 2.

    V. Bruk, “A class of boundary-value problems with the spectral parameter in the limit condition,” Mat. Sb.,100, No. 2, 210–216 (1976).

  3. 3.

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

  4. 4.

    V. A. Derkach and M. M. Malamud, “The Weil function of a Hermitian operator and its relation to the characteristic function,” Preprint DonFTI-85-9 (104) Academy of Sciences of the Ukrainian SSR, Donetsk (1985).

  5. 5.

    M. G. Krein, “Theory of self-adjoint extensions of semibounded operators and its applications. I, II,” Mat. Sb.,20, No. 3, 431–495 (1947); ibid.,21, No. 3, 365–404 (1947).

  6. 6.

    Yu. M. Arlinskii, “Accretive (*)-extensions of a positive-symmetric operator,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 11, 3–5 (1980).

  7. 7.

    A. N. Kochubei, “Extensions of a positive-definite symmetric operator,” ibid., No. 3, 168–171 (1979).

  8. 8.

    V. A. Mikhailets, “Operator Spectra and Boundary Value Problems,” Spectral Analysis of Differential Operators [in Russian], Inst. of Math. of the Academy of Sciences of the Ukr. SSR, Kiev (1980), pp. 106–131.

  9. 9.

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

  10. 10.

    Yu. M. Arlinskii and É. P. Tsekanovskii, “Sectorial extensions of positive-Hermitian operators and their resolvents,” Dokl. Akad. Nauk Arm. SSR,79, No. 5, 199–202 (1984).

  11. 11.

    V. Yu. Kolmanovich and M. M. Malamud, “Extensions of sectorial operators and dual pairs of contradictions,” to appear in VINITI, Donetsk (1985), No. 4428-85 Dep.

  12. 12.

    V. A. Derkach, M. M. Malamud, and É. P. Tsekanovskii, “Sectorial extensions of a positive operator, and the characteristic function,” to appear in UkrNIINTI, Donetsk (1986). No. 214-UK87.

Download references

Author information

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 1, pp. 8–14, January–February, 1988.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Arlinskii, Y.M. Positive spaces of boundary values and sectorial extensions of a nonnegative symmetric operator. Ukr Math J 40, 5–10 (1988). https://doi.org/10.1007/BF01056437

Download citation

Keywords

  • Symmetric Operator
  • Positive Space
  • Sectorial Extension
  • Nonnegative Symmetric Operator