由内部谱数据确定的扩散算子的反问题

Inverse Problem for Diffusion Operators from Interior Spectral Data

研究了有限区间[0,π]上的扩散算子的反问题,证明如果已知边界条件中的系数h,则部分特征函数在(0,π)内某点的函数值及二组谱的部分谱能够惟一确定势函数(q,p)及边界条件中的系数H.

In this paper, we discuss the inverse problem for diffusion operators on the finite interval [0, π] from interior spectral data and show that if coei^icient h of the boundary condition is known a priori, then the potentials （q,p） and coefficient H of the boundary condition can be uniquely determined by a set of values of eigenfunctions at some interior point and parts of two spectra.