蜘蛛状量子图上的布朗运动
Brownian Motion on The Spider Like Quantum Graphs
AI总结：
本文对蜘蛛状量子图上的布朗运动进行概率分析，研究N条半轴在原点以基尔霍夫条件连接的扩散极限定理，并给出蜘蛛图拉普拉斯算子谱测度及广义傅里叶变换的相关性质。
摘要：
本文对最简单量子图——蜘蛛图上的布朗运动进行了概率分析：该系统由N条半轴仅在图的原点通过最简单的（即所谓的基尔霍夫）粘合条件连接而成。在此类图上的扩散极限定理，特别是当N趋于无穷时，与经典情形N=2（全轴）有显著不同。额外的结果涉及蜘蛛图拉普拉斯算子的谱测度性质及相应的广义傅里叶变换。本文的续篇将研究蜘蛛图上薛定谔算子类的谱：由无界势扰动的拉普拉斯算子及相关的相变。
英文摘要：
The paper contains the probabilistic analysis of the Brownian motion on the simplest quantum graph, spider: a system of N-half axis connected only at the graph's origin by the simplest (so-called Kirchhoff's) gluing conditions. The limit theorems for the diffusion on such a graph, especially if $N \to \infty$ are significantly different from the classical case $N = 2$ (full axis). Additional results concern the properties of the spectral measure of the spider Laplacian and the corresponding generalized Fourier transforms. The continuation of the paper will contain the study of the spectrum for the class of Schrödinger operators on the spider graphs: Laplacian perturbed by unbounded potential and related phase transitions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
