Sturm-Liouville problems and global bounds by small control sets and applications to quantum graphs

被引：0

作者：

Egidi, Michela ^{[1
]}

Mugnolo, Delio ^{[2
]}

Seelmann, Albrecht ^{[3
]}

机构：

[1] Univ Rostock, Inst Math, D-18051 Rostock, Germany

[2] Fern Univ Hagen, Fak Math & Informat, Lehrgebiet Anal, D-58084 Hagen, Germany

[3] Tech Univ Dortmund, Fak Math, D-44221 Dortmund, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 535卷 / 01期

关键词：

Spectral geometry; Sturm-Liouville problems; Magnetic Schrodinger operators; Unique continuation property; Eigenfunctions of quantum graphs; Control theory; INEQUALITY; LOCALIZATION; EQUATIONS; THEOREM;

D O I：

10.1016/j.jmaa.2024.128101

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a Logvinenko-Sereda theory for one-dimensional vector-valued selfadjoint operators. We thus deliver upper bounds on L-2-norms of eigenfunctions - and linear combinations thereof - in terms of their L-2- and W-1,W-2-norms on small control sets that are merely measurable and suitably distributed along each interval. An essential step consists in proving a Bernstein-type estimate for Laplacians with rather general vertex conditions. Our results carry over to a large class of Schrodinger operators with magnetic potentials; corresponding results are unknown in higher dimension. We illustrate our findings by discussing the implications in the theory of quantum graphs.

引用

页数：32

共 61 条

[1]

Alphonse P, 2023, Arxiv, DOI arXiv:2212.10842

[2] Quantum ergodicity on graphs: From spectral to spatial delocalization [J].