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Nanosystems: Physics, Chemistry, Mathematics, 2018, Volume 9, Issue 2, Pages 215–224 (Mi nano155)  
MATHEMATICS

Inverse dynamic problems for canonical systems and de Branges spaces

A. S. Mikhailovab, V. S. Mikhailovab

a St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 7 Fontanka, St. Petersburg, 191023 Russia
b St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034 Russia
Full-text PDF (216 kB)
Abstract: We show the equivalence of inverse problems for different dynamical systems and corresponding canonical systems. For canonical system with general Hamiltonian we outline the strategy of studying the dynamic inverse problem and procedure of construction of corresponding de Branges space.
Keywords: inverse problem, Boundary Control method, de Branges spaces, Schrödinger operator, Dirac system, Jacobi matrices, canonical systems.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00529-A
17-01-00099-A
18-01-00269-A
Volkswagen Foundation
The research of Victor Mikhaylov was supported in part by RFBR 17-01-00529-A. Alexandr Mikhaylov was supported by RFBR 17-01-00099-A; A. S. Mikhaylov and V. S. Mikhaylov were partly supported by RFBR 18-01-00269-A and VW Foundation program “Modeling, Analysis, and Approximation Theory toward application in tomography and inverse problems”.
Received: 08.01.2018
Revised: 19.01.2018
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. S. Mikhailov, V. S. Mikhailov, “Inverse dynamic problems for canonical systems and de Branges spaces”, Nanosystems: Physics, Chemistry, Mathematics, 9:2 (2018), 215–224
Citation in format AMSBIB
\Bibitem{MikMik18}
\by A.~S.~Mikhailov, V.~S.~Mikhailov
\paper Inverse dynamic problems for canonical systems and de Branges spaces
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2018
\vol 9
\issue 2
\pages 215--224
\mathnet{http://mi.mathnet.ru/nano155}
\elib{https://elibrary.ru/item.asp?id=32760272}
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