Dynamical inverse problem for Jacobi matrices

A. S. Mikhaylov; V. S. Mikhaylov

Dynamical inverse problem for Jacobi matrices

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arxiv 1704.02481 v1 pith:DT7ZKOSZ submitted 2017-04-08 math.SP

A. S. Mikhaylov , V. S. Mikhaylov This is my paper · ORCID

classification math.SP

keywords inversedynamicalproblemdiscretejacobilinemeasuresemi-infinite

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We consider the inverse dynamical problem for the dynamical system with discrete time associated with the semi-infinite Jacobi matrix. We solve the inverse problem for such a system and answer a question on the characterization of the inverse data. As a by-product we give a necessary and sufficient condition for the measure on the real line line to be the spectral measure of semi-infinite discrete Schrodinger operator.

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Inverse dynamic problems for canonical systems and de Branges spaces
math.AP 2025-05 conditional novelty 4.0 of 10

The authors show that dynamic inverse problems for wave, Dirac and Jacobi systems are equivalent to inverse problems for canonical systems, and outline a dynamic de Branges space construction.

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