论文标题
通过操作员和算法的无限图形的谐波分析不变性
Harmonic analysis invariants for infinite graphs via operators and algorithms
论文作者
论文摘要
我们介绍了无限图的谐波分析的最新进展。我们的方法将组合工具与希尔伯特空间，几何，边界结构和光谱不变的无界遗产经营者理论的新结果结合在一起。我们专注于特定类别的无限图，包括在电网络模型中出现的加权图以及新的图形图表。我们进一步强调了我们目前对无限图的分析，一方面是潜在理论，傅立叶二元性，概率，谐波函数，采样/插值和边界理论的特定领域。随着使用极限结构，无限和本地化的限制结构，我们概述了我们在无限图表的结果如何被视为香农理论的扩展：从可数的无限图$ g $开始，以及适当的固定正重功能，以及一个conterua（某些Ambients $ x $ $ g $ g $ g）（$ x $ g）（$ x $ g $ g）（$ x $ g）的功能（$ x $ g $ g）（他们对离散图$ g $的限制。
We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral invariants. We focus on particular classes of infinite graphs, including such weighted graphs which arise in electrical network models, as well as new diagrammatic graph representations. We further stress some direct parallels between our present analysis on infinite graphs, on the one hand, and, on the other, specific areas of potential theory, Fourier duality, probability, harmonic functions, sampling/interpolation, and boundary theory. With the use of limit constructions, finite to infinite, and local to global, we outline how our results for infinite graphs may be viewed as extensions of Shannon's theory: Starting with a countable infinite graph $G$, and a suitable fixed positive weight function, we show that there are certain continua (certain ambient sets $X$) extending $G$, and associated notions of interpolation for (Hilbert spaces of) functions on $X$ from their restrictions to the discrete graph $G$.
