solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看1932次
An inverse problem for Sturm-Liouville operators on trees with partial information given on the potentials. (arXiv:1711.05659v1 [math.SP])
来源于:arXiv
We consider Sturm-Liouville operators on geometrical graphs without cycles
(trees) with singular potentials from the class $W_2^{-1}$. We suppose that the
potentials are known on a part of the graph, and study the so-called partial
inverse problem, which consists in recovering the potentials on the remaining
part of the graph from some parts of several spectra. The main results of the
paper are the uniqueness theorem and a constructive procedure for the solution
of the partial inverse problem. Our method is based on the completeness and the
Riesz-basis property of special systems of vector functions, and the reduction
of the partial inverse problem to the complete one on a part of the graph. 查看全文>>