标题： 逆Sturm-Liouville问题在量子树上的稳定性 显示英文标题

标题： Stability of the inverse Sturm-Liouville problem on a quantum tree

摘要： 本文讨论了在度量树上具有空间$W_2^{-1}$分布势的Sturm-Liouville算子。 我们研究了一个逆谱问题，即从与各种边界条件相关的特征函数中恢复势函数。 我们证明了对于任何固定半径的球中的势函数，该逆问题的均匀稳定性，以及在谱数据的小扰动下的局部稳定性。 我们的方法基于一种稳定的算法，用于唯一重建势函数，该算法依赖于谱映射方法的思想。 显示英文摘要

摘要： This paper deals with the Sturm-Liouville operators with distribution potentials of the space $W_2^{-1}$ on a metric tree. We study an inverse spectral problem that consists in the recovery of the potentials from the characteristic functions related to various boundary conditions. We prove the uniform stability of this inverse problem for potentials in a ball of any fixed radius, as well as the local stability under small perturbations of the spectral data. Our approach is based on a stable algorithm for the unique reconstruction of the potentials relying on the ideas of the method of spectral mappings.