Gaps between consecutive eigenvalues for compact metric graphs

被引：1

作者：

Borthwick, David ^{[1
]}

Harrell II, Evans M. ^{[2
]}

Yu, Haozhe ^{[1
]}

机构：

[1] Emory Univ, Dept Math, Atlanta, GA 30322 USA

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 531卷 / 01期

关键词：

Spectral theory; Quantum graphs; Eigenvalue gap; SPECTRAL GAP; INEQUALITIES;

D O I：

10.1016/j.jmaa.2023.127802

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

On a compact metric graph, we consider the spectrum of the Laplacian defined with a mix of standard and Dirichlet vertex conditions. A Cheeger-type lower bound on the gap lambda 2 - lambda 1 is established, with a constant that depends only on the total length of the graph and minimum edge length. We also prove some improvements of known upper bounds for eigenvalue gaps and ratios for metric trees and extensions to certain other types of graphs.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：26

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