Essential Self-Adjointness of the Laplacian on Weighted Graphs: Harmonic Functions, Stability, Characterizations and Capacity

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-05-26 DOI:10.1007/s11040-025-09498-z

Atsushi Inoue, Sean Ku, Jun Masamune, Radosław K. Wojciechowski

引用次数: 0

Abstract

We give two characterizations for the essential self-adjointness of the weighted Laplacian on birth–death chains. The first involves the edge weights and vertex measure and is classically known; however, we give another proof using stability results, limit point-limit circle theory and the connection between essential self-adjointness and harmonic functions. The second characterization involves a new notion of capacity. Furthermore, we also analyze the essential self-adjointness of Schrödinger operators, use the characterizations for birth–death chains and stability results to characterize essential self-adjointness for star-like graphs, and give some connections to the \(\ell ^2\)-Liouville property.

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加权图上拉普拉斯算子的本质自伴随性：调和函数、稳定性、刻画和容量

给出了生-死链上加权拉普拉斯算子的本质自伴随性的两个刻画。第一种方法涉及边缘权重和顶点度量，这是经典的；然而，我们利用稳定性结果、极限点-极限圆理论以及本质自伴随与调和函数之间的联系，给出了另一种证明。第二个特征涉及一个新的能力概念。此外，我们还分析了Schrödinger算子的本质自伴随性，利用生灭链的刻画和稳定性结果刻画了星形图的本质自伴随性，并给出了\(\ell ^2\) -Liouville性质的一些联系。

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

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.