Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs
Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs
复制标题
度量图谱最小划分的交错和 Friedlander 型不等式
DOI：
10.1007/s11005-021-01438-6
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发表时间：
2021
影响因子：
1.2
通讯作者：
J. Kennedy
中科院分区：
文献类型：
--
作者：
Matthias Hofmann;J. Kennedy
我们证明了建立在Dirichlet和标准Laplacian特征值上的度量图的谱最小能量之间的交织不等式，正如最近在Kennedy等人中介绍的那样。（Calc Var PDE 60：61，2021）。这些不等式，其中涉及的第一贝蒂数和度1顶点的图，回顾交织和其他不等式的拉普拉斯特征值的整个图，以及估计的节点和诺依曼域的数目之间的差异，整个图的特征函数。为此，我们仔细研究的原则，切割一个图形，特别是量化的大小削减作为扰动的原始图形通过其排名的概念。作为推论，我们得到这些能量和实际的Dirichlet和标准拉普拉斯特征值之间的不等式，有效的所有紧凑的图形，这补充了一个版本的树图的Friedlander的不等式之间的Dirichlet和诺依曼特征值的域。在某些情况下，这会导致更好的拉普拉斯特征值估计比以前通过更直接的方法获得的。
We prove interlacing inequalities between spectral minimal energies of metric graphs built on Dirichlet and standard Laplacian eigenvalues, as recently introduced in Kennedy et al. (Calc Var PDE 60:61, 2021). These inequalities, which involve the first Betti number and the number of degree one vertices of the graph, recall both interlacing and other inequalities for the Laplacian eigenvalues of the whole graph, as well as estimates on the difference between the number of nodal and Neumann domains of the whole graph eigenfunctions. To this end we study carefully the principle of cutting a graph, in particular quantifying the size of a cut as a perturbation of the original graph via the notion of its rank. As a corollary we obtain an inequality between these energies and the actual Dirichlet and standard Laplacian eigenvalues, valid for all compact graphs, which complements a version for tree graphs of Friedlander’s inequalities between Dirichlet and Neumann eigenvalues of a domain. In some cases this results in better Laplacian eigenvalue estimates than those obtained previously via more direct methods.
影响因子：
1.3
作者：
G. Berkolaiko;J. Kennedy;P. Kurasov;Delio Mugnolo
通讯作者：
G. Berkolaiko;J. Kennedy;P. Kurasov;Delio Mugnolo