Direct and inverse spectral problems for rank-one perturbations of self-adjoint operators

Oles Dobosevych; Rostyslav Hryniv

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Direct and inverse spectral problems for rank-one perturbations of self-adjoint operators

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arxiv 2007.08841 v1 pith:LMFZ44HL submitted 2020-07-17 math.SP

Oles Dobosevych , Rostyslav Hryniv This is my paper · ORCID

classification math.SP

keywords inverseperturbationsrank-oneself-adjointspectrumcharacterizecompletelydirect

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abstract

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

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