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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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Online
ISSN
1569-3945
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Volume 24, Issue 3

Issues

Recovery of the matrix quadratic differential pencil from the spectral data

Natalia Bondarenko
Published Online: 2015-04-16 | DOI: https://doi.org/10.1515/jiip-2014-0074

Abstract

We consider a pencil of matrix Sturm–Liouville operators on a finite interval. We study the properties of its spectral characteristics and inverse problems that consist in the recovering of the pencil by the spectral data, that is, eigenvalues and so-called weight matrices. This inverse problem is reduced to a linear equation in a Banach space by the method of spectral mappings. A constructive algorithm for the solution of the inverse problem is provided.

Keywords: Matrix quadratic differential pencils; spectral data; inverse spectral problems; method of spectral mappings

MSC: 34A55; 34B07; 34B24; 34L40; 47E05

About the article

Received: 2014-10-31

Revised: 2015-01-21

Accepted: 2015-01-24

Published Online: 2015-04-16

Published in Print: 2016-06-01


Funding Source: Ministry of Education and Science of the Russian Federation

Award identifier / Grant number: 1.1436.2014K

Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 13-01-00134

Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 14-01-31042

Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 15-01-04864

This research was supported by Grant 1.1436.2014K of the Ministry of Education and Science of the Russian Federation and by Grants 13-01-00134, 14-01-31042 and 15-01-04864 of the Russian Foundation for Basic Research.


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 24, Issue 3, Pages 245–263, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2014-0074.

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[1]
Natalia Bondarenko
Analysis and Mathematical Physics, 2017, Volume 7, Number 1, Page 77

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