衰减保持算子与本质谱的稳定性
谱理论
2007-05-23 v2 偏微分方程分析
摘要
我们建立了在 Banach 模上作用的无界算子的本质谱稳定性的判据。其应用涵盖在非光滑流形或局部紧阿贝尔群上向量纤维丛的截面作用的算子，特别是欧氏空间上具复可测系数的任意阶微分算子、奇异 Dirac 算子，以及具可测度量的黎曼流形上的 Laplace-Beltrami 算子。
引用
@article{arxiv.math/0411489,
title = {Decay Preserving Operators and Stability of the Essential Spectrum},
author = {Vladimir Georgescu and Sylvain Golenia},
journal= {arXiv preprint arXiv:math/0411489},
year = {2007}
}
备注
This revised version differs from the original one in three respects: 1. Several improvements of the stability criteria for operators in divergence form on an Euclidean space and for Laplace operators on Riemannian manifolds. 2. New references and comments clarify the class of manifolds to which our abstract results can be applied. 2. A rather important reorganization of the paper should make it more readable