Dynamic inverse problem for Jacobi matrices

Александр Сергеевич Михайлов, Виктор Сергеевич Михайлов

Research output

1 Citation (Scopus)

Abstract

We consider the inverse dynamic problem for a dynamical system with discrete time associated with a semi-infinite Jacobi matrix. We derive discrete analogs of Krein equations and answer a question on the characterization of dynamic inverse data. As a consequence we obtain a necessary and sufficient condition for a measure on a real line to be a spectral measure of a semi-infinite discrete Schrödinger operator.
Original languageEnglish
Pages (from-to)431-447
Number of pages17
JournalInverse Problems and Imaging
Volume13
Issue number3
DOIs
Publication statusPublished - 2019

Fingerprint

Inverse Dynamics
Jacobi Matrix
Dynamic Problem
Inverse problems
Inverse Problem
Discrete Operators
Infinite Matrices
Spectral Measure
Real Line
Dynamical systems
Discrete-time
Dynamical system
Analogue
Necessary Conditions
Sufficient Conditions

Cite this

Михайлов, Александр Сергеевич ; Михайлов, Виктор Сергеевич. / Dynamic inverse problem for Jacobi matrices. In: Inverse Problems and Imaging. 2019 ; Vol. 13, No. 3. pp. 431-447.
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Dynamic inverse problem for Jacobi matrices. / Михайлов, Александр Сергеевич; Михайлов, Виктор Сергеевич.

In: Inverse Problems and Imaging, Vol. 13, No. 3, 2019, p. 431-447.

Research output

TY - JOUR

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AU - Михайлов, Александр Сергеевич

AU - Михайлов, Виктор Сергеевич

PY - 2019

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AB - We consider the inverse dynamic problem for a dynamical system with discrete time associated with a semi-infinite Jacobi matrix. We derive discrete analogs of Krein equations and answer a question on the characterization of dynamic inverse data. As a consequence we obtain a necessary and sufficient condition for a measure on a real line to be a spectral measure of a semi-infinite discrete Schrödinger operator.

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DO - 10.3934/ipi.2019021

M3 - Article

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SN - 1930-8337

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