On the inverse spectral theory of Schrödinger and Dirac operators (Q2723469)
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scientific article; zbMATH DE number 1614739
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the inverse spectral theory of Schrödinger and Dirac operators |
scientific article; zbMATH DE number 1614739 |
Statements
On the inverse spectral theory of Schrödinger and Dirac operators (English)
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5 July 2001
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inverse spectral problems
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spectral function
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Weyl function
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Schrödinger operator
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Dirac operator
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0.94400597
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0.9365868
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0.9319048
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0.9313511
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0.9300016
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0.92972124
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Let \(\sigma_j\), \(j=1,\dots,N\), be the spectra of the boundary value problem NEWLINE\[NEWLINE -y''+q(x)y=\lambda y,\quad 0<x<\pi, NEWLINE\]NEWLINE NEWLINE\[NEWLINE y(0)\cos\alpha_j + y'(0)\sin\alpha_j =0, \qquad y(\pi)\cos\beta + y'(\pi)\sin\beta =0, NEWLINE\]NEWLINE where \(q(x)\in L_1(0,\pi)\) is real, \(0\leq\alpha_j<\pi\), \(0\leq\beta<\pi\). Let \(a\in [0,\pi)\), and \(S_j\subset\sigma_j\). Under some conditions it is proved that the specification of \(S_j\), \(j=1,\dots,N\), and \(q\) on \((0,a)\) uniquely determines \(q\) on \((a,\pi)\).
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