论文标题
曲线多边形的逆向斯特克洛夫光谱问题
Inverse Steklov spectral problem for curvilinear polygons
论文作者
论文摘要
本文研究了曲线多边形的逆向斯特克洛夫光谱问题。对于具有小于$π$的一般曲线多边形的通用曲线多边形，我们证明在Arxiv中获得的Steklov Eigenvalues的渐近学：1908.06455以建设性的方式确定了顶点的数量和侧面长度的正确有序序列，以及某些等效性的相互关系。如果通用假设失败，我们还向本语句提供反例。特别是，我们表明存在渐近接近steklov光谱的非等级三角形。在其他技术中，我们使用Hadamard-WeierStrass化定理的版本，使我们能够从其根的渐近学中重建三角函数。
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 arXiv:1908.06455 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.
