Spectral properties of Sturm–Liouville operators on infinite metric graphs

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-11 DOI:10.1007/s13324-024-00937-8

Yihan Liu, Jun Yan, Jia Zhao

引用次数: 0

Abstract

This paper mainly deals with the Sturm–Liouville operator

$$\begin{aligned} \textbf{H}=\frac{1}{w(x)}\left( -\frac{\textrm{d}}{\textrm{d}x}p(x)\frac{ \textrm{d}}{\textrm{d}x}+q(x)\right) ,\text { }x\in \Gamma \end{aligned}$$

acting in $L_{w}^{2}\left( \Gamma \right) ,$ where $\Gamma $ is a metric graph. We establish a relationship between the bottom of the spectrum and the positive solutions of quantum graphs, which is a generalization of the classical Allegretto–Piepenbrink theorem. Moreover, we prove the Persson-type theorem, which characterizes the infimum of the essential spectrum.

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无限度量图上 Sturm-Liouville 算子的谱特性

本文主要讨论 Sturm-Liouville 算子 $$\begin{aligned}\textbf{H}=\frac{1}{w(x)}\left( -\frac{\textrm{d}}{\textrm{d}x}p(x)\frac{ \textrm{d}}{\textrm{d}x}+q(x)\right) ,\在 $L_{w}^{2}left( \Gamma \right) ,$ 中起作用，其中 $\Gamma $ 是一个度量图。我们在谱底和量子图的正解之间建立了一种关系，这是对经典的 Allegretto-Piepenbrink 定理的概括。此外，我们还证明了佩尔松型定理，该定理描述了本质谱的下底。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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