论文标题
三阶自动差差异操作员具有周期性边界条件和非本地电势的直接和反向问题
Direct and inverse problems for a third order self-adjoint differential operator with periodic boundary conditions and nonlocal potential
论文作者
论文摘要
已经考虑了具有周期性边界条件和一维扰动的三阶自动差异差异操作员。对于该运算符，我们首先表明频谱由简单的特征值组成，有限的多种特征值二。然后描述了本征函数和解决方案的表达。最后，解决了恢复一维扰动的所有组件的逆问题。特别是，我们证明了Ambarzumyan型定理，并表明可以通过三个光谱重建均匀或奇数的电位。
A third order self-adjoint differential operator with periodic boundary conditions and an one-dimensional perturbation has been considered. For this operator, we first show that the spectrum consists of simple eigenvalues and finitely many eigenvalues of multiplicity two. Then the expressions of eigenfunctions and resolvent are described. Finally, the inverse problems for recovering all the components of the one-dimensional perturbation are solved. In particular, we prove the Ambarzumyan-type theorem and show that the even or odd potential can be reconstructed by three spectra.
