Abstract
Bu çalışmada, standart teknik kullanılarak, sağ yarı eksende tanımlanan vektör-fonksiyonlarının ağırlıklı Hilbert uzayında birinci mertebeden özel tip lineer diferansiyel-operatör ifadesi tarafından üretilen minimal ve maksimal operatörleri yapılandırdık. Bu durumda, minimal operatör akretif olup maksimal değildir. Bu çalışmadaki asıl amacımız, vektör fonksiyonlarının ağırlıklı Hilbert uzayında, minimal operatörün tüm maksimal akretif genişlemelerinin genel formunu tanımlamaktır. Calkin-Gorbachuk metodu kullanılarak, bu minimal operatörün tüm maksimal akretif genişlemelerinin genel gösterimi sınır değerleri dilinde ifade edilmiştir. Ayrıca bu minimal operatörün maksimal akretif genişlemelerinin spektrum yapısı araştırılmıştır.
References
- Gorbachuk, V.L. and Gorbachuk, M.L., Boundary value problems for operator differential equations, Kluwer Academic Publisher, Dordrecht, (1991).
- Kato, T., Perturbation theory for linear operators, Springer-Verlag Inc., New York, (1966).
- Levchuk, V.V., Smooth maximally dissipative boundary-value problems for a parabolic equation in a Hilbert Space, Ukrainian Mathematic Journal, 35, 4, 502-507, (1983).
- Hörmander, L., On the theory of general partial differential operators, Acta Mathematica, 94, 161-248, (1955).
- Naimark, M.A., Linear differential operators, Frederick Ungar Publishing Company, New York, USA, (1968).
Abstract
In the present paper, we construct the minimal and maximal operators generated by special type linear differential-operator expression for first order in the weighted Hilbert space of vector-functions defined on right semi-axis with the use of standard technique. In this case, the minimal operator is accretive but not maximal. Our main goal in this paper is to describe the general form of all maximally accretive extensions of the minimal operator in the weighted Hilbert space of vector-functions. Using the Calkin-Gorbachuk method, the general representation of all maximally accretive extensions of this minimal operator in terms of boundary conditions is obtained. We also investigate the structure of the spectrum set such maximally accretive extensions of this type of minimal operator.
Keywords
Accretive operator differential operator deficiency index space of boundary values spectrum
References
- Gorbachuk, V.L. and Gorbachuk, M.L., Boundary value problems for operator differential equations, Kluwer Academic Publisher, Dordrecht, (1991).
- Kato, T., Perturbation theory for linear operators, Springer-Verlag Inc., New York, (1966).
- Levchuk, V.V., Smooth maximally dissipative boundary-value problems for a parabolic equation in a Hilbert Space, Ukrainian Mathematic Journal, 35, 4, 502-507, (1983).
- Hörmander, L., On the theory of general partial differential operators, Acta Mathematica, 94, 161-248, (1955).
- Naimark, M.A., Linear differential operators, Frederick Ungar Publishing Company, New York, USA, (1968).
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | April 10, 2020 |
| Submission Date | November 4, 2019 |
| Published in Issue | Year 2020 Volume: 22 Issue: 2 |