Dynamical inverse problem for the discrete Schrödinger operator

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.