Abstract
In this paper, using the Calkin-Gorbachuk method, the general form of all maximal dissipative extensions of the minimal operator generated by first order linear multipoint symmetric singular differential-operator expression in the direct sum of Hilbert space of vector-functions has been found. Later on, the structure of spectrum of these extensions is researched. Finally, the results are supported by an application.
Keywords
Dissipative differential operator selfadjoint differential operator deficiency index space of boundary values spectrum
References
- Bairamov, E., Öztürk Mert, R., Ismailov, Z. I., Selfadjoint extensions of a singular differential operator, J. Math. Chem., 50 (2012), 1100-1110.
- Fischbacher, C., On the theory of dissipative extensions. PhD, University of Kent School of Mathematics, Statistic and Actuarial Science, Canterbury, England, 2017.
- Gorbachuk, V. I., Gorbachuk, M. L., Boundary Value Problems for Operator Differential Equations, Dordrecht, the Netherlands, Kluwer Academic Publishers, 1991.
- Hörmander, L., On the theory of general partial differential operators, Acta Mathematica, 94 (1955), 161-248.
- Ismailov, Z. I., Ipek, P., Selfadjoint singular differential operators of first order and their spectrum, Electronic Journal of Differential Equations, 21 (2016), 1-9.
- Nagy, Sz. B., Foias, C., Analyse Harmonique des Operateurs de L' espace de Hilbert, Masson, Paris and Akad Kiodo, Budapest, 1997, English transl. North-Holland, Amesterdam and Akad Kiado, Budapest, 1970.
- Naimark, M. A., Linear Differential Operators, New York, USA, Frederick Ungar Publishing Company, 1968.
- Rofe-Beketov, F. S., Kholkin, A. M., Spectral Analysis of Differential Operators, USA, World Scientific Monograph Series in Mathematics 7, 2005.
- von Neumann, J., Allgemeine eigenwerttheories hermitescher funktionaloperatoren, Mathematische Annalen, 102 (1929-1930), 49-131 (in German).
Abstract
References
- Bairamov, E., Öztürk Mert, R., Ismailov, Z. I., Selfadjoint extensions of a singular differential operator, J. Math. Chem., 50 (2012), 1100-1110.
- Fischbacher, C., On the theory of dissipative extensions. PhD, University of Kent School of Mathematics, Statistic and Actuarial Science, Canterbury, England, 2017.
- Gorbachuk, V. I., Gorbachuk, M. L., Boundary Value Problems for Operator Differential Equations, Dordrecht, the Netherlands, Kluwer Academic Publishers, 1991.
- Hörmander, L., On the theory of general partial differential operators, Acta Mathematica, 94 (1955), 161-248.
- Ismailov, Z. I., Ipek, P., Selfadjoint singular differential operators of first order and their spectrum, Electronic Journal of Differential Equations, 21 (2016), 1-9.
- Nagy, Sz. B., Foias, C., Analyse Harmonique des Operateurs de L' espace de Hilbert, Masson, Paris and Akad Kiodo, Budapest, 1997, English transl. North-Holland, Amesterdam and Akad Kiado, Budapest, 1970.
- Naimark, M. A., Linear Differential Operators, New York, USA, Frederick Ungar Publishing Company, 1968.
- Rofe-Beketov, F. S., Kholkin, A. M., Spectral Analysis of Differential Operators, USA, World Scientific Monograph Series in Mathematics 7, 2005.
- von Neumann, J., Allgemeine eigenwerttheories hermitescher funktionaloperatoren, Mathematische Annalen, 102 (1929-1930), 49-131 (in German).
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | June 30, 2020 |
| Submission Date | November 5, 2019 |
| Acceptance Date | April 28, 2020 |
| Published in Issue | Year 2020 Volume: 69 Issue: 1 |
Cite
Cited By
Maximally Dissipative Differential Operators of First Order in the Weighted Hilbert Space
Lobachevskii Journal of Mathematics
https://doi.org/10.1134/S1995080221030033
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
