Abstract
A method is proposed to describe the maximal nonnegative and the proper maximal accretive extensions of a nonnegative closed densely defined operator in a Hilbert space.
Literature cited
M. G. Krein, “The theory of self-adjoint extensions of semibounded operators,” Mat. Sb.,20, No. 3, 431–495 (1947).
V. I. Gorbachuk and M. I. Gorbachuk, Boundary-Value Problems for Operator-Differential Equations [in Russian], Naukova Dumka, Kiev (1984).
A. N. Kochubei, “On extensions of a positive definite operator,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 3, 168–171 (1979).
V. É. Lyantse and O. G. Storozh, Methods of the Theory of Unbounded Operators [in Russian], Naukova Dumka, Kiev (1983).
V. A. Derkach and M. M. Malamud, “The Weyl function of a Hermitian operator and its connection with the characteristic function,” Preprint 85-9 (104), Akad. Nauk UkrSSR, Donetsk Physicotechnical Institute, Donetsk (1985).
A. V. Shtraus, “On extensions of a semibounded operator,” Dokl. Akad. Nauk SSSR,231, No. 3, 543–546 (1983).
V. A. Mikhailets, “The spectra of operators, and boundary-value problems,” in: Spectral Analysis of Differential Operators [in Russian], Akad. Nauk UkrSSR, Inst. Math., Kiev (1980), pp. 106–131.
O. G. Storozh, “A description of some classes of extensions of a nonnegative operator,” Dop. Akad. Nauk UkrRSR, Ser. A, No. 10, 14–16 (1987).
A. N. Kochubei, “On the characteristic functions of symmetric operators and their extensions,” Izv. Akad. Nauk ArmSSR,15, No. 3, 219–232 (1980).
V. A. Derkach, M. M. Malamud, and É. R. Tsekanovskii, “The sectorial extensions of a positive operator, and the characteristic function,” Dokl. Akad. Nauk SSSR,298, No. 1, 537–541 (1988).
Yu. M. Arlinskii, “Positive spaces of boundary values, and the sectorial extensions of a nonnegative symmetric operator,” Ukr. Mat. Zh.,40, No. 1, 8–14 (1988).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 858–860, June, 1990.
Rights and permissions
About this article
Cite this article
Storozh, O.G. Extremal extensions of a nonnegative operator, and accretive boundary-value problems. Ukr Math J 42, 758–760 (1990). https://doi.org/10.1007/BF01058931
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058931