Abstract
For a singular differential operator with arbitrary equal deficiency indices, the space of boundary values is constructed and the corresponding Weyl function is determined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. I. Gorbachuk and M. L. Gorbachuk,Boundary-Value Problems for Differential Operator Equations [in Russian], Naukova Dumka, Kiev (1984).
V. A. Derkach and M. M. Malamud, “Generalized resolvents and boundary-value problems for Hermitian operators with gaps,”J. Funct. Anal.,95, No. 1, 1–95 (1991).
F. S. Rofe-Beketov, “On self-adjoint extensions of differential operators in the space of vector functions,”Teor. Funkts. Anal.,8, 3–24 (1969).
A. M. Hol'kin, “Description of extensions of differential operators on an infinite interval in the indefinite case,”Teor. Funkts. Anal. Prilozhen.,44, 112–122 (1985).
F. G. Maksudov and B. P. Allakhverdiev, “On extensions of the Schrödinger operator with matrix potentials,”Dokl. Akad. Nauk SSSR,332, No. 1, 18–20 (1993).
V. I. Mogilevskii, “On proper extensions of a singular differential operator in the space of vector functions,”Dokl. Akad. Nauk Ukr., Ser. A, No. 9, 29–34 (1994).
M. A. Naimark,Linear Differential Operators [in Russian], Nauka, Moscow (1969).
V. A. Derkach and M. M. Malamud, “Characteristic functions of almost solvable extensions of Hermitian operators,”Ukr. Mat. Zh.,44, No. 4, 435–459 (1992).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 671–685, May, 1995.
The author expresses his deep gratitude to M. M. Malamud for helpful discussions.
Rights and permissions
About this article
Cite this article
Mogilevskii, V.I. On proper extensions of a singular differential operator in the space of vector functions. Ukr Math J 47, 773–788 (1995). https://doi.org/10.1007/BF01059050
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01059050