Krymski, S;
Levitin, M;
Parnovski, L;
Polterovich, I;
Sher, DA;
(2021)
Inverse Steklov spectral problem for curvilinear polygons.
International Mathematics Research Notices
, 2021
(1)
pp. 1-37.
10.1093/imrn/rnaa200.
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Abstract
This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than π, we prove that the asymptotics of Steklov eigenvalues obtained in [ 20] determines, in a constructive manner, the number of vertices and the properly ordered sequence of side lengths, as well as the angles up to a certain equivalence relation. We also present counterexamples to this statement if the generic assumptions fail. In particular, we show that there exist non-isometric triangles with asymptotically close Steklov spectra. Among other techniques, we use a version of the Hadamard–Weierstrass factorization theorem, allowing us to reconstruct a trigonometric function from the asymptotics of its roots.
| Type: | Article |
|---|---|
| Title: | Inverse Steklov spectral problem for curvilinear polygons |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imrn/rnaa200 |
| Publisher version: | http://dx.doi.org/10.1093/imrn/rnaa200 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10107885 |
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