Schrodinger operators with locally integrable potentials on infinite metric graphs

被引：7
|
作者：
Akduman, Setenay [1 ]
Pankov, Alexander [2 ]
机构：
[1] Dokuz Eylul Univ, Dept Math, Izmir, Turkey
[2] Morgan State Univ, Dept Math, Baltimore, MD 21239 USA
来源：
APPLICABLE ANALYSIS | 2017年 / 96卷 / 12期
关键词：
Metric graph; Schrodinger operator; spectrum; QUANTUM GRAPHS; SPECTRUM;
D O I：
10.1080/00036811.2016.1207247
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper is devoted to Schrodinger operators on infinite metric graphs. We suppose that the potential is locally integrable and its negative part is bounded in certain integral sense. First, we obtain a description of the bottom of the essential spectrum. Then we prove theorems on the discreteness of the negative part of the spectrum and of the whole spectrum that extend some classical results for one dimensional Schrodinger operators.
引用
收藏
页码：2149 / 2161
页数：13
相关论文
共 50 条
  • [1] Exponential decay of eigenfunctions of Schrodinger operators on infinite metric graphs
    Akduman, Setenay
    Pankov, Alexander
    COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2017, 62 (07) : 957 - 966
  • [2] Spectral properties of Sturm-Liouville operators on infinite metric graphs
    Liu, Yihan
    Yan, Jun
    Zhao, Jia
    ANALYSIS AND MATHEMATICAL PHYSICS, 2024, 14 (04)
  • [3] Nonlinear Schrodinger equation with growing potential on infinite metric graphs
    Akduman, Setenay
    Pankov, Alexander
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 184 : 258 - 272
  • [4] Eigenfunction Expansions for Schrodinger Operators on Metric Graphs
    Lenz, Daniel
    Schubert, Carsten
    Stollmann, Peter
    INTEGRAL EQUATIONS AND OPERATOR THEORY, 2008, 62 (04) : 541 - 553
  • [5] Eigenvalue estimates for Schrodinger operators on metric trees
    Ekholm, Tomas
    Frank, Rupert L.
    Kovarik, Hynek
    ADVANCES IN MATHEMATICS, 2011, 226 (06) : 5165 - 5197
  • [6] Spectral properties of combinatorial Schrodinger operators on infinite weighted graphs
    Akkouche, Sofiane
    ASYMPTOTIC ANALYSIS, 2011, 74 (1-2) : 1 - 31
  • [7] Optimal Wegner estimates for random Schrodinger operators on metric graphs
    Gruber, Michael J.
    Helm, Mario
    Veselic, Ivan
    ANALYSIS ON GRAPHS AND ITS APPLICATIONS, 2008, 77 : 409 - +
  • [8] TRACE FORMULAE FOR SCHRODINGER OPERATORS ON METRIC GRAPHS WITH APPLICATIONS TO RECOVERING MATCHING CONDITIONS
    Ershova, Yulia
    Kiselev, Alexander V.
    METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2014, 20 (02): : 134 - 148
  • [9] Spectral determinants and zeta functions of Schrodinger operators on metric graphs
    Harrison, J. M.
    Kirsten, K.
    Texier, C.
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (12)
  • [10] SCHRODINGER OPERATORS ON GRAPHS: SYMMETRIZATION AND EULERIAN CYCLES
    Karreskog, G.
    Kurasov, P.
    Kupersmidt, I. Trygg
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (03) : 1197 - 1207
12345