Geodesic
Functional Models in De Branges Spaces of One Class Commutative Operators
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2014), pp. 430-450.

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For a commutative system of the linear bounded operators $ T_1$, $T_2 $, which operate in the Hilbert space $ H $ and none of the operators $ T_1$, $T_2 $ is a compression, the functional model is constructed. The model is built for a circle in de Branges space. 
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V. N. Syrovatskyi. Functional Models in De Branges  Spaces of One Class Commutative Operators. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2014), pp. 430-450. http://geodesic.mathdoc.fr/item/JMAG_2014_10_a3/

[1] M. S. Livshits, A. A. Yantsevich, Theory of Operator Knots in Hilbert Spaces, Izdat. Kharkiv Univ., Kharkov, 1971 (Russian) | MR | Zbl

[2] V. A. Zolotarev, Analytical Methods of Spectral Representation of Non-unitary and Non-selfadjoint Operators, Kharkiv National University, Kharkov, 2003 (Russian)

[3] Lui De Branges, Hilbert Spaces of Entire Functions, Prentice-Hall, London, 1968 | MR

[4] M. S. Livshits, “About one Class of Linear Operators in Hilbert Space”, Math. Collection, 19:2 (1946), 236–260

[5] B. S. Nagy, C. Foias, Harmonic Analysis of Operators in Hilbert Space, Mir, M., 1970 (Russian) | MR | Zbl

[6] V. A. Zolotarev, V. N. Syrovatsky, “De Branges Transform on the Cicle”, Vestnik KNU V. N. Karazin. Series “Mathematics and Applied Mechanics”, 2005, no. 711 (Russian)

[7] V. A. Zolotarev, “Model Representations of Commutative Systems of Linear Operators”, Funct. Anal. and Appl., 22:1 (1988), 66–68 | DOI | MR | Zbl

[8] V. A. Zolotarev, “Functional Model of Commutative Operator Systems”, J. Math. Phys., Anal., Geom., 4:3 (2008), 420–440 | MR | Zbl

[9] V. N. Syrovatsky, “Functional Models of Commutative Systems of Operators Close to the Unitary”, Vestnik KNU V. N. Karazin. Series “Mathematics and Applied Mechanics”, 2012, no. 1018 (Russian)