扰动Cayley树的调和分析
Harmonic analysis on perturbed Cayley Trees
摘要：
本文研究了非均匀网络上约瑟夫森结阵列的纯跳跃模型的玻色爱因斯坦凝聚的数学问题。所研究的图是通过在齐次凯莱树上添加密度为零的扰动而得到的。生成的拓扑模型由图上的邻接运算符（与之相反）描述。本文研究了扰动网络邻接的一些相关谱性质，如低于范数的隐谱的出现、瞬时性和Perron Frobenius分布。所有提到的性质本身都有数学意义，并且在研究所考虑的网络上的巴伯-库珀玻色子的BEC时有自然的应用。
英文摘要：
We study the mathematical aspects of the Bose Einstein Condensation for the pure hopping model describing arrays of Josephson junctions on non homogeneous networks. The graphs under investigation are obtained by adding density zero perturbations to the homogeneous Cayley Trees. The resulting topological model is described by the (opposite of the) adjacency operator on the graph. In the present paper we investigate some relevant spectral properties of the adjacency of the perturbed network, such the appearance of the hidden spectrum below the norm, the transience character and the Perron Frobenius distribution. All the mentioned properties have a mathematical interest in itself, and have natural applications for the investigation of the BEC of Bardeen Cooper Bosons on the networks under consideration.
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。
