Dynamical inverse problem for the discrete Schrödinger operator

2025/05/26 by Mikhaylov, A. S. · 4 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2505.19711

Abstract

We consider the inverse problem for the dynamical system with discrete Schrödinger operator and discrete time. As an 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.

Citations

• On some applications of the Boundary Control method to spectral estimation and inverse problems
• The boundary control approach to inverse spectral theory

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• Forward and inverse problems for a finite Krein-Stieltjes string. Approximation of constant density by point masses

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