| Title | About functional models of commutative systems of operators in the spaces of de Branges |
| Publication Type | Journal Article |
| Year of Publication | 2017 |
| Authors | Syrovatskyi, VN |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2017.04.007 |
| Issue | 4 |
| Section | Mathematics |
| Pagination | 7-11 |
| Date Published | 4/2017 |
| Language | Russian |
| Abstract | For the commutative system of linear bounded operators T1, T2 which act in a Hilbert space H and are such that none of them is a compression, a functional model is built in the space of de Branges for a circle. |
| Keywords | commutative system of operators, functional model |
References:
- Zolotarev, V. A. (2008). Functional model of commutative operator systems. J. Math. Physics, Analysis, Geometry, 4, No 3, pp. 420-440.
- Sirovatsky, V. N. (2012). Functional models for commutative systems of operators close to a unitary one. Kharkov University Bulletin, No 1018, pp. 41-61 (in Russian).
- Syrovatskyi, V. N. (2014). Functional Models in De Branges Spaces of One Class Commutative Operators. J. Math. Physics, Analysis, Geometry, 10, No 4, pp. 430-450.
- Zolotarev, V. A., Sirovatsky, V. N. (2005). Transformation de Branges on the terms. Kharkov University Bulletin, No 711, Iss. 55, pp. 80-92 (in Russian).
- Livshits, M. S., Yantsevich, A. A. (1971). A theory of operator knots in Hilbert spaces. Kharkov: Izd-vo Kharkov. un-ta (in Russian).
- Zolotarev, V. A. (2003). Analytical methods of spectral presentations of not self-conjugate and nonunitary operators. Kharkov: Izd-vo Kharkov. un-ta (in Russian).
- Zolotarev, V. A. (1988). Model representations of commutative systems of linear operators. Functional Analysis and Its Applications, 22, Iss. 1, pp. 55-57. https://doi.org/10.1007/BF01077726
