najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2018-9-2-215-224najo-696Research ArticleMATHEMATICSМАТЕМАТИКАInverse dynamic problems for canonical systems and de Branges spacesMikhaylovA. S.

7 Fontanka, St. Petersburg, 191023

7/9 Universitetskaya nab., St. Petersburg, 199034 

mikhaylov@pdmi.ras.ruMikhaylovV. S.

7 Fontanka, St. Petersburg, 191023

7/9 Universitetskaya nab., St. Petersburg, 199034 

vsmikhaylov@pdmi.ras.ruSt. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences; St. Petersburg State UniversityRussian Federation20181208202592215–224Copyright © Mikhaylov A.S., Mikhaylov V.S., 20252025Mikhaylov A.S., Mikhaylov V.S.Mikhaylov A.S., Mikhaylov V.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/696

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.

inverse problemBoundary Control methodde Branges spacesSchrodinger operatorDirac systemJacobi matricescanonical systemsThe 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.ReferencesMikhaylov A.S., Mikhaylov V.S. The Boundary Control method and de Branges spaces. Schrodinger equation, Dirac system and Discrete¨ Schrodinger operator.¨ Journal of Mathematical Analysis and Applications, 2018, 460 (2), P. 927–953.Mikhaylov A.S., Mikhaylov V.S. The Boundary Control method and de Branges spaces. 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The authors declare that there are no conflicts of interest present.