Inverse eigenvalue problem for a simple star graph
Inverse eigenvalue problem for a simple star graph
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DOI：
10.4171/jst/101
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发表时间：
2015-06
期刊：
影响因子：
--
通讯作者：
W. Rundell;P. Sacks
中科院分区：
文献类型：
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作者：
W. Rundell;P. Sacks
可以通过识别间隔为 R 的边来为图定义薛定谔算子和相关谱，在边上定义系数函数，在内部顶点处施加适当的匹配条件，在外部顶点处施加适当的边界条件。继 Pivovarchik [14] 的早期工作之后，我们考虑由在单个点相交的三个等长边组成的图的逆特征值问题，其中谱数据是图的狄利克雷特征值以及三个单独边的狄利克雷谱。我们推导、讨论和演示一种建设性的解决方法，获得另一种唯一性证明，并讨论几种概括。数学学科分类（2010）。 34B24、34A50、34A55、34L05、81Q10。
A Schrödinger operator and associated spectra may be de ned for a graph by identifying edges with intervals of R, on which coe cient functions are de ned, imposing appropriate matching conditions at the internal vertices and boundary conditions at the external vertices. Following earlier work of Pivovarchik [14], we consider an inverse eigenvalue problem for a graph consisting of three equal length edges meeting at a single point, where the spectral data is the Dirichlet eigenvalues of the graph together with the Dirichlet spectra of the three individual edges. We derive, discuss and demonstrate a constructive solution method, obtain an alternative uniqueness proof, and discuss several kinds of generalizations. Mathematics Subject Classi cation (2010). 34B24, 34A50, 34A55, 34L05, 81Q10.