Inverse eigenvalue problems for a damped Stieltjes string with mixed data

In this paper, we consider the inverse eigenvalue problem for a Stieltjes string subject to the Robin condition at the left end and a damping condition at the right end with mixed data, which consists of the values of a part of masses and lengths and a subset of its spectrum. We use Krein-Nudelman&#...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 601; pp. 55 - 71
Main Authors Yang, Lu, Guo, Yongxia, Wei, Guangsheng
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.09.2020
American Elsevier Company, Inc
Subjects
Complex numbers
Damped vibrations
Damping
Eigenvalues
Interpolation
Interpolation formula
Inverse problem
Inverse problems
Linear algebra
Stieltjes string
Strings
secondary
Stieltjes string
Interpolation formula
Damped vibrations
primary
Inverse problem
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ISSN0024-3795
1873-1856
DOI10.1016/j.laa.2020.04.023

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Summary:In this paper, we consider the inverse eigenvalue problem for a Stieltjes string subject to the Robin condition at the left end and a damping condition at the right end with mixed data, which consists of the values of a part of masses and lengths and a subset of its spectrum. We use Krein-Nudelman's interpolation formula for a rational S-function to deal with our problem. We present a decomposition of the S0-function associated with the Stieltjes string, which makes it possible to use Krein-Nudelman's interpolation formula. Necessary and sufficient conditions are given for existence and uniqueness of solution to the inverse problem such that a finite number of simple not purely imaginary complex numbers lying in the open upper half-plane are a subset of the spectrum of a damped Stieltjes string.
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ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2020.04.023