Dynamical inverse problem for the discrete Schr\"odinger operator
Analysis of PDEs
2025-05-27 v1 Spectral Theory
Abstract
We consider the inverse problem for the dynamical system with discrete Schr\"odinger operator and discrete time. As an inverse data we take a \emph{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 \emph{response operators} of the dynamical system governed by the discrete Schr\"odinger operator.
Cite
@article{arxiv.2505.19711,
title = {Dynamical inverse problem for the discrete Schr\"odinger operator},
author = {A. S. Mikhaylov and A. S. Mikhaylov},
journal= {arXiv preprint arXiv:2505.19711},
year = {2025}
}