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arXiv · 2505.08339

Unified approach to classical equations of inverse problem theory

M. I. Belishev·V. S. Mikhaylov
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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.

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M. I. Belishev, V. S. Mikhaylov. 2025-05-13. Unified approach to classical equations of inverse problem theory. https://doi.org/10.1515/jip-2012-0040

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