Dynamical inverse problem for the discrete Schrödinger operator
https://doi.org/10.17586/2220-8054-2016-7-5-842-853
Abstract
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.
Keywords
inverse problem,
discrete Schrödinger operator,
Boundary Control method,
characterization of inverse data
Supporting agencies: The 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’.
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, 191023, St. Petersburg
7/9 Universitetskaya nab., 199034, St. Petersburg
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, 191023, St. Petersburg
7/9 Universitetskaya nab., 199034, St. Petersburg
References
1. Belishev M.I. Recent progress in the boundary control method. Inverse Problems, 2007, 23 (5), R1.
2. 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.
3. Belishev M.I. C*-Algebras in reconstruction of manifolds. Nanosystems: Phys. Chem. Math., 2013, 4 (4), P. 484–489.
4. Avdonin S.A., Mikhaylov V.S. The boundary control approach to inverse spectral theory. Inverse Problems, 2010, 26 (4), 045009, 19 p.
5. 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. 461–488
Review
For citations:
Mikhaylov A.S., Mikhaylov V.S. Dynamical inverse problem for the discrete Schrödinger operator. Nanosystems: Physics, Chemistry, Mathematics. 2016;7(5):842-853. https://doi.org/10.17586/2220-8054-2016-7-5-842-853
Views:
4
Email this article 