Inverse Steklov Spectral Problem for Curvilinear Polygons

This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than $\pi $, we prove that the asymptotics of Steklov eigenvalues obtained in [ 20] determines, in a constructive manner, the number of vertices and the properly ordere...

Full description

Saved in:
Bibliographic Details
Published in:International mathematics research notices 2021-01, Vol.2021 (1), p.1-37
Main Authors: Krymski, Stanislav, Levitin, Michael, Parnovski, Leonid, Polterovich, Iosif, Sher, David A
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than $\pi $, 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.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnaa200