论文标题
异态逆问题
Isomorphic inverse problems
论文作者
论文摘要
考虑在单位间隔上Sturm-Liouville问题的两个反问题。这意味着从希尔伯特（Hilbert）空间中有两个相应的映射$ f，f $，在他们的光谱数据中有$ h $。如果$ f $是$ f $的成分，而某些同构$ u $ $ $ h $ a自身。同构类是彼此同构的逆问题的集合。我们在单位间隔和圆上考虑了基本的Sturm-Liouville问题，并描述了它们的逆问题的同构类别。例如，我们证明Dirichlet和Neumann边界条件的情况是同构的。证明基于非线性分析。
Consider two inverse problems for Sturm-Liouville 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. A isomorphic class is a collection of inverse problems isomorphic to each other. We consider basic Sturm-Liouville problems on the unit interval and on the circle and describe their isomorphic classes of inverse problems. For example, we prove that the inverse problems for the case of Dirichlet and Neumann boundary conditions are isomorphic. The proof is based on the non-linear analysis.
