najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2016-7-5-842-853najo-948Research ArticleСтатьиDynamical inverse problem for the discrete Schrödinger operatorMikhaylovA. S.

7, Fontanka, 191023, St. Petersburg

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

a.mikhaylov@spbu.ruMikhaylovV. S.

7, Fontanka, 191023, St. Petersburg

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

v.mikhaylov@spbu.ruSt. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences; St. Petersburg State UniversityRussian Federation20161508202575842853Copyright © 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/948

We consider the inverse problem for the dynamical system with discrete Schrödinger operator and discrete time. As inverse data, we take a response operator, the natural analog of the dynamical Dirichlet-to-Neumann map. We derive two types of equations of inverse problem and answer a question on the characterization of the inverse data, i.e. we describe the set of operators, which are response operators of the dynamical system governed by the discrete Schrödinger operator.

inverse problemdiscrete Schrödinger operatorBoundary Control methodcharacterization of inverse dataThe research of Victor Mikhaylov was supported in part by NIR SPbGU 11.38.263.2014 and RFBR 14-01-00535. Alexandr Mikhaylov was supported by RFBR 14-01-00306; A.S. Mikhaylov and V.S. Mikhaylov were partly supported by VW Foundation program ‘Modeling, Analysis, and Approximation Theory toward application in tomography and inverse problems’.ReferencesBelishev M.I. Recent progress in the boundary control method. Inverse Problems, 2007, 23 (5), R1.Belishev M.I. Recent progress in the boundary control method. Inverse Problems, 2007, 23 (5), R1.Avdonin S.A., Mikhaylov A.S., Mikhaylov V.S. On some applications of the Boundary Control method to spectral estimation and inverse problems. Nanosystems: Phys. Chem. Math., 2015, 6 (1), P. 63–78.Avdonin S.A., Mikhaylov A.S., Mikhaylov V.S. On some applications of the Boundary Control method to spectral estimation and inverse problems. Nanosystems: Phys. Chem. Math., 2015, 6 (1), P. 63–78.Belishev M.I. C*-Algebras in reconstruction of manifolds. Nanosystems: Phys. Chem. Math., 2013, 4 (4), P. 484–489.Belishev M.I. C*-Algebras in reconstruction of manifolds. Nanosystems: Phys. Chem. Math., 2013, 4 (4), P. 484–489.Avdonin S.A., Mikhaylov V.S. The boundary control approach to inverse spectral theory. Inverse Problems, 2010, 26 (4), 045009, 19 p.Avdonin S.A., Mikhaylov V.S. The boundary control approach to inverse spectral theory. Inverse Problems, 2010, 26 (4), 045009, 19 p.Belishev M.I., Mikhailov V.S. Unified approach to classical equations of inverse problem theory. Journal of Inverse and Ill-Posed Problems, 2012, 20 (4), P. 461–488Belishev M.I., Mikhailov V.S. Unified approach to classical equations of inverse problem theory. Journal of Inverse and Ill-Posed Problems, 2012, 20 (4), P. 461–488

The authors declare that there are no conflicts of interest present.