论文标题
关于星形图的下属理论
Subordinacy Theory on Star-Like Graphs
论文作者
论文摘要
我们在类似星形的图上研究雅各比矩阵，这些图是通过将有限数量的半线粘贴到紧凑型图的图形。具体而言，我们将下属理论扩展到这种类型的图形，也就是说，我们发现解决方案的渐近性能与特征值方程的渐近性能与光谱度量相对于Lebesgue度量的频谱度量的连续性。我们还使用该理论来得出有关奇异频谱多样性的结果。
We study Jacobi matrices on star-like graphs, which are graphs that are given by the pasting of a finite number of half-lines to a compact graph. Specifically, we extend subordinacy theory to this type of graphs, that is, we find a connection between asymptotic properties of solutions to the eigenvalue equations and continuity properties of the spectral measure with respect to the Lebesgue measure. We also use this theory in order to derive results regarding the multiplicity of the singular spectrum.
