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Nanosystems: Phys. Chem. Math., 2022, 13 (1), 24–29

On the construction of de Branges spaces for dynamical systems associated with finite Jacobi matrices

Alexander S. Mikhaylov – St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 191023 St. Petersburg; St. Petersburg State University, 199034 St. Petersburg, Russia; mikhaylov@pdmi.ras.ru
Victor S. Mikhaylov – St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 191023 St. Petersburg, Russia; vsmikhaylov@pdmi.ras.ru

Corresponding author: Alexander S. Mikhaylov, mikhaylov@pdmi.ras.ru

ABSTRACT We consider dynamical systems with boundary control associated with finite Jacobi matrices. Using the method previously developed by the authors, we associate with these systems special Hilbert spaces of analytic functions (de Branges spaces).

KEYWORDS Boundary control method, Krein equations, Jacobi matrices, de Branges spaces

ACKNOWLEDGEMENTS A. S. Mikhaylov and V.S. Mikhaylov were partly supported by Volkswagen Foundation project “From Modeling and Analysis to Approximation”.

FOR CITATION Mikhaylov A.S., Mikhaylov V.S. On the construction of de Branges spaces for dynamical systems associated with finite Jacobi matrices. Nanosystems: Phys. Chem. Math., 2022, 13 (1), 24–29.

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