Abstract/Summary

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 [LPPS19] 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 factorisation theorem, allowing us to reconstruct a trigonometric function from the asymptotics of its roots.