Inverse problems associated with the Hill operator (Q2794408)
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scientific article; zbMATH DE number 6553510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inverse problems associated with the Hill operator |
scientific article; zbMATH DE number 6553510 |
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10 March 2016
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Hill operator
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inverse spectral theory
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eigenvalue asymptotics
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Fourier coefficients
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Inverse problems associated with the Hill operator (English)
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The author investigates an inverse problem connected with the Hill operator. NEWLINEHe proves an Ambarzumyan-type theorem such that, if the asypmtotic behaviour of the lenght of the \(n\)-th instability interval \((l_{n}=o(n^{-2}))\) and the properties of the subset of the periodic spectrum of the Hill operator are given then the potential \(q\) vanishes almost everywhere on \((0,1)\). NEWLINEHe also proves a similar theorem for the anti-periodic case.
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