Literature cited
T. Kato, Perturbation Theory for Linear Operators, Springer, New York (1966).
S. G. Krein, Linear Differential Equations in Banach Space, Am. Math. Soc., Providence (1971).
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).
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).
M. G. Krein, “The theory of selfadjoint extensions of semibounded operators,” Mat. Sb.,20 (62), No. 3, 431–498 (1947).
A. N. Kochubei, “Extensions of a positive definite symmetric operator,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 3, 168–171 (1979).
V. I. Gorbachuk and M. L. Gorbachuk, Boundary Value Problems for Differential-Operator Equations [in Russian], Naukova Dumka, Kiev (1984).
V. A. Mikhailets, Spectra of operators and boundary value problems,” in: Spectral Analysis of Differential Operators [in Russian], Kiev (1980), pp. 106–131.
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).
T. Ando and K. Nishio, “Positive self-adjoint extensions of positive symmetric operators,” Tohoku Math. J.,22, 65–75 (1970).
A. V. Shtrus, “Characteristic functions of linear operators,” Izv. Akad. Nauk SSSR, Ser. Mat.,24, No. 1, 43–74 (1960).
M. A. Naimark, Linear Differential Operators [in Russian], Nauka, Moscow (1969).
M. M. Malamud and é. R. Tsekanovskii, On sectorial extensions of positive operators. Makeevka (1984). [Manuscript deposited at VINITI, No. 4585.]
é. R. Tsekanovskii, “The characteristic function and sectorial boundary-value problems,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 21–24 (1985).
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).
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).
A. V. Shtraus, “On the extensions of a semibounded operator,” Dokl. Akad. Nauk SSSR,221, No. 3, 543–546 (1973).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 2, pp. 151–158, February, 1989.
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01060376