无限度量图上 Sturm-Liouville 算子的谱特性

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

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引用次数: 0

摘要

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。

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Spectral properties of Sturm–Liouville operators on infinite metric graphs

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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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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.