Green's function asymptotics of periodic elliptic operators on abelian coverings of compact manifolds
Green's function asymptotics of periodic elliptic operators on abelian coverings of compact manifolds
复制标题
紧流形阿贝尔覆盖上周期椭圆算子的格林函数渐近
DOI：
10.1016/j.jfa.2017.10.016
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
M. Kha
中科院分区：
文献类型：
--
作者：
M. Kha
本文的主要结果给出了具有交换甲板群的非紧黎曼余紧覆盖上“一般”周期二阶自伴椭圆算子的格林函数在谱间隙边缘附近和在谱间隙边缘的无穷远渐近性态。以前，已知类似的结果仅适用于Rn的情况。发现的一个有趣的特征是，甲板组的等级比流形的尺寸起到更重要的作用。
The main results of this article provide asymptotics at infinity of the Green's functions near and at the spectral gap edges for “generic” periodic second-order, self-adjoint, elliptic operators on noncompact Riemannian co-compact coverings with abelian deck groups. Previously, analogous results have been known for the case of R n only. One of the interesting features discovered is that the rank of the deck group plays more important role than the dimension of the manifold.