[0，1]上径向薛定谔算子的逆谱问题
Inverse spectral problem for radial Schrödinger operator on [0, 1]
摘要：
对于单位区间上一类具有显奇异性$a(a + 1)/x^2, a \in \mathbb{N}$的奇异Sturm-Liouville方程，考虑了一个谱反问题.我们的目标是通过$λ^a$指出的光谱数据和$κ^a$指出的一些赋范常数对势进行全局参数化。对于$a = 0$和$a=1$，已知$λ^a\times κ^a$是$\lr$上的全局坐标系。借助于变换算子，我们将这一结果推广到任意非负整数$a$，并给出了等谱集的一种描述。
英文摘要：
For a class of singular Sturm-Liouville equations on the unit interval with explicit singularity $a(a + 1)/x^2, a \in \mathbb{N}$, we consider an inverse spectral problem. Our goal is the global parametrization of potentials by spectral data noted by $λ^a$, and some norming constants noted by $κ^a$. For $a = 0$ and $a=1$, $λ^a\times κ^a$ was already known to be a global coordinate system on $\lr$. With the help of transformation operators, we extend this result to any non-negative integer $a$ and give a description of isospectral sets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
