Inverse dynamic problems for canonical systems and de Branges spaces
https://doi.org/10.17586/2220-8054-2018-9-2-215-224
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,
Schrodinger operator,
Dirac system,
Jacobi matrices,
canonical systems
Supporting agencies: 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 1801-00269-A and VW Foundation program “Modeling, Analysis, and Approximation Theory toward application in tomography and inverse problems”. The authors are deeply indebted to Prof. R. V. Romanov and Prof. M.I. Belishev for valuable discussions.
About the Authors
A. S. Mikhaylov
St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences; St. Petersburg State University
Russian Federation
Russian Federation
7 Fontanka, St. Petersburg, 191023
7/9 Universitetskaya nab., St. Petersburg, 199034
V. S. Mikhaylov
St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences; St. Petersburg State University
Russian Federation
Russian Federation
7 Fontanka, St. Petersburg, 191023
7/9 Universitetskaya nab., St. Petersburg, 199034
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Review
For citations:
Mikhaylov A.S., Mikhaylov V.S. Inverse dynamic problems for canonical systems and de Branges spaces. Nanosystems: Physics, Chemistry, Mathematics. 2018;9(2):215–224. https://doi.org/10.17586/2220-8054-2018-9-2-215-224
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