{"title":"Subordinacy theory on star-like graphs","authors":"Netanel Levi","doi":"10.4171/jst/450","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":48789,"journal":{"name":"Journal of Spectral Theory","volume":"37 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/jst/450","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
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.
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.
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