标题： 半直线上的逆共振问题的稳定性 显示英文标题

标题： Stability of Inverse Resonance Problem on the Half Line

摘要： 我们考虑一维散射理论中的逆共振问题。 散射矩阵由$2\times 2$个亚纯函数的条目组成，这些是某些傅里叶变换的商。 共振被表示为波场傅里叶变换的零点。 对于紧支撑扰动，我们能够定量估计每个亚纯条目的零点和极点。 势函数支撑的大小与散射波场的零点分布相关。 我们基于对共振扰动理论的某些知识，推导了基于散射源的逆稳定性。 当共振分布规律时，通过值分布理论存在某种自然稳定性。 显示英文摘要

摘要： We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed as the zeros of Fourier transform of wave field. For compactly-supported perturbation, we are able to quantitatively estimate the zeros and poles of each meromorphic entry. The size of potential support is connected to the zero distribution of scattered wave field. We derive the inverse stability on scattering source based on certain knowledge on the perturbation theory of resonances. When the resonances are distributed regularly, there is certain natural stability through the value distribution theory.