1Storozh, OG 1Ivan Franko National University of Lviv |
Dopov. Nac. akad. nauk Ukr. 2018, 4:3-8 |
https://doi.org/10.15407/dopovidi2018.04.003 |
Section: Mathematics |
Language: Ukrainian |
Abstract: In the terms of abstract boundary operators and corresponding Weyl functions, the resolvent set of the socalled proper extensions of closed linear relations in a Hilbert space is established, and the resolvents of the mentioned extensions are constructed. The results are applied to the case where the initial relation is the graph of the finitedimensional restriction of a closed densely defined operator. |
Keywords: extension, Hilbert space, linear relation, resolvent |
References:
- Arens, R. (1961). Operational calculus of linear relations. Pacif. J. Math., 11, No. 1, pp. 923. doi: https://doi.org/10.2140/pjm.1961.11.9
- Coddington, E. A. (1973). Selfadjoint subspace extensions of nondensely defined linear symmetric operators. Bull. Amer. Math. Soc., 79, No. 4, pp. 712-715. doi: https://doi.org/10.1090/S0002-9904-1973-13275-6
- Dijksma, A. & Snoo, H. S. V. de. (1974). Selfadjoint extensions of symmetric subspaces. Pacif. J. Math., 54, No. 1, pp. 71-100. doi: https://doi.org/10.2140/pjm.1974.54.71
- RofeBeketov, F. S. (1969). Selfadjoint extensions of differential operators in the spase of vectorfunctions. Dokl. AN SSSR, 184, No. 5, pp. 1034-1037 (in Russian).
- Kochubei, A. N. (1975). Extensions of symmetric operators and symmetric linear relations. Mat. Zametki, 17, No. 1, pp. 41-48 (in Russian).
- Gorbachuk, V. I. & Gorbachuk, M. L. (1984). Boundary value problems for differentialoperator equations. Kiev: Naukova Dumka (in Russian).
- Krasnoselskij, M. A. (1949). On selfadjoint extensions of Hermitian operators. Ukr. Math. Zhurn., No. 1, pp. 21-38 (in Russian).
- Strauss, A. W. (1968). On extensions and characteristic function of symmetric operator. Izv. AN SSSR, 32, No. 1, pp. 186-207 (in Russian).
- Kochubei, A. N. (1977). The extensions of a nondensely defined symmetric operator. Sib. Math. J., 18, No. 2, pp. 225-229. doi: https://doi.org/10.1007/BF00967155
- Derkach, V. A. & Mamalud, M. M. (1995). The extension theory of Hermitian operators and the moment problem. J. Math. Sci, 73, No. 2, pp. 141-242. doi: https://doi.org/10.1007/BF02367240
- Malamud, M. M. & Mogilevskii, V. I. (1997). On extensions of dual pairs of operators. Dopov. Nac. acad. nauk Ukr., No. 1, pp. 30-37 (in Ukrainian).
- Olijar, Yu. I. & Storozh, O. G. (2013). Abstract boundary operators and some classes of extensions of linear relations. Dopov. Nac. acad. nauk Ukr., No. 4, pp. 19-22 (in Ukrainian).
- Kato, T. (1972). Perturbation theory for linear operators. Moscow: Mir (in Russian).
- Oliyar, Yu. I. & Storozh, O. G. (2014). On a criteria of mutual adjoiness for extensions of some nondensely definedoperators. Meth. Funct. Anal. Topol., 20, No. 1, pp. 50-58.
- Storozh, O. G. (1995). Extension theory methods and differentialboundary operators. (Unpublished Doctor thesis). Ivan Franko Lviv State University, Lviv, Ukraine (in Ukrainian).