关于加权图上拉普拉斯算子自伴扩张的一个注记
泛函分析
2013-07-02 v2
摘要
我们研究加权图上拉普拉斯算子的自伴扩张与 Markov 扩张的唯一性。首先证明，对于局部有限图和某类度量，图的完备性蕴含这些扩张的唯一性。此外，当图非度量完备且 Cauchy 边界具有有限容量时，我们刻画了 Markov 扩张的唯一性。
引用
@article{arxiv.1208.6358,
title = {A note on self-adjoint extensions of the Laplacian on weighted graphs},
author = {Xueping Huang and Matthias Keller and Jun Masamune and Radosław K. Wojciechowski},
journal= {arXiv preprint arXiv:1208.6358},
year = {2013}
}
备注
17 pages. The assumption of "finite jump size" found in Theorems 1 and 2 in the previous version has been replaced by a weaker condition concerning the newly introduced notion of a "combinatorial neighborhood" in Theorem 1 and has been removed altogether from Theorem 2. Some references added. Final version to appear in J. Funct. Anal