Dynamical inverse problem for the discrete Schrödinger operator
https://doi.org/10.17586/2220-8054-2016-7-5-842-853
Аннотация
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.
Об авторах
A. Mikhaylov
St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences; St. Petersburg State University
Россия
Россия
V. Mikhaylov
St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences; St. Petersburg State University
Россия
Россия
Список литературы
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
Рецензия
Для цитирования:
, . Наносистемы: физика, химия, математика. 2016;7(5):842-853. https://doi.org/10.17586/2220-8054-2016-7-5-842-853
For citation:
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
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