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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2016, 7 (5), P. 842–853

Dynamical inverse problem for the discrete Schrödinger operator

A. S. Mikhaylov – St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 7, Fontanka, 191023, St. Petersburg; St. Petersburg State University, 7/9 Universitetskaya nab., 199034, St. Petersburg, Russia; a.mikhaylov@spbu.ru
V. S. Mikhaylov – St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 7, Fontanka, 191023, St. Petersburg; St. Petersburg State University, 7/9 Universitetskaya nab., 199034, St. Petersburg, Russia; v.mikhaylov@spbu.ru

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.

DOI 10.17586/2220-8054-2016-7-5-842-853

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