Direct and Inverse Spectral Problems for Rank-One Perturbations of Self-adjoint Operators

For a given self-adjoint operator A with discrete spectrum, we completely characterise possible eigenvalues of its rank-one perturbations  B and discuss the inverse problem of reconstructing B from its spectrum.

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Bibliographic Details
Published in:Integral equations and operator theory 2021-04, Vol.93 (2), Article 18
Main Authors: Dobosevych, Oles, Hryniv, Rostyslav
Format: Article
Language:English
Subjects:
Analysis
Eigenvalues
Inverse problems
Mathematics
Mathematics and Statistics
Perturbation
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Description
Summary:For a given self-adjoint operator A with discrete spectrum, we completely characterise possible eigenvalues of its rank-one perturbations  B and discuss the inverse problem of reconstructing B from its spectrum.
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-021-02630-y