星形图的从属理论

IF 1 3区数学 Q1 MATHEMATICS

Journal of Spectral Theory Pub Date : 2023-09-13 DOI:10.4171/jst/450

Netanel Levi

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引用次数: 1

摘要

我们研究了星形图上的Jacobi矩阵，星形图是由有限数量的半线粘贴到紧图上得到的图。具体地说，我们将隶属理论推广到这类图中，即我们发现了特征值方程解的渐近性质与谱测度相对于勒贝格测度的连续性性质之间的联系。我们也用这个理论来推导关于奇异谱的多重性的结果。

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Subordinacy theory on star-like graphs

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.

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来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.