Unified approach to classical equations of inverse problem theory
Analysis of PDEs
2025-05-14 v1 Spectral Theory
Abstract
The boundary control (BC-) method is an approach to inverse problems based upon their deep relations to control and system theory. We show that the classical integral equations of inverse problem theory (Gelfand-Levitan, Krein and Marchenko equations) can be derived in the framework of the BC-method in a unified way. Namely, to solve each of these equations is in fact to solve a relevant boundary control problem, whereas its solution is determined by the inverse data.
Keywords
Cite
@article{arxiv.2505.08339,
title = {Unified approach to classical equations of inverse problem theory},
author = {M. I. Belishev and V. S. Mikhaylov},
journal= {arXiv preprint arXiv:2505.08339},
year = {2025}
}