ZS算子的反问题及其同构性
Inverse problems for ZS-operators and their isomorphisms
AI总结：
本文研究了ZS算子在单位区间和环上的同构反问题，通过非线性分析和4谱映射的性质，探讨了算子的同构性及其在不同边界条件下的应用。
摘要：
考虑在单位区间上ZS算子的两个反问题。这意味着存在两个相应的映射F, f从势函数的Hilbert空间H到其谱数据。如果F是f和某个将H映射到自身的同构算子U的复合，则称为同构。我们考虑在单位区间上以及在环上，对于基本边界条件的ZS算子的同构反问题。证明基于非线性分析和本文中构造的4谱映射的性质。
英文摘要：
Consider two inverse problems for ZS-operators problems on the unit interval. It means that there are two corresponding mappings $F, f$ from a Hilbert space of potentials $H$ into their spectral data. They are called isomorphic if $F$ is a composition of $f$ and some isomorphism $U$ of $H$ onto itself. We consider isomorphic inverse problems for ZS-operators on the unit interval under basic boundary conditions and on the circle. The proof is based on the non-linear analysis and properties of the 4-spectra mapping constructed in our paper.
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。
