About functional models of commutative systems of operators in the spaces of de Branges

Authors

  • V.N. Syrovatskyi V. N. Karazin Kharkiv National University

DOI:

https://doi.org/10.15407/dopovidi2017.04.007

Keywords:

commutative system of operators, functional model

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.

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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

Published

01.07.2024

How to Cite

Syrovatskyi, V. (2024). About functional models of commutative systems of operators in the spaces of de Branges . Reports of the National Academy of Sciences of Ukraine, (4), 7–11. https://doi.org/10.15407/dopovidi2017.04.007