A characterization of circles by single layer potentials (Q1687852)
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scientific article; zbMATH DE number 6821937
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of circles by single layer potentials |
scientific article; zbMATH DE number 6821937 |
Statements
A characterization of circles by single layer potentials (English)
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4 January 2018
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Let \(\Omega\) be a smoothly bounded domain in the plane, and assume that the single-layer potential \[ f\mapsto -\frac{1}{2\pi}\int_{\partial\Omega}f(\zeta)\ln|z - \zeta|\,ds \] on \(L^{2}(\partial\Omega, ds)\) has a polynomial eigenfunction such that all its zeros belong to \(\Omega\). Then \(\partial\Omega\) must be a circle.
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single-layer potential
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polynomial eigenfunction
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0.7380288243293762
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