摘要
本文对无穷维Hamilton算子的谱理论及相关问题的研究情况做一综述,内容包括无穷维Hamilton算子的特征展开定理、谱理论、可逆性和可逆补等.本文还提出了一些待解决的问题.
The paper is a survey on the spectrum and related problems of infinite dimesional Hamiltonian operators, which involves in the expansion theorem in terms of the system of eigenfunctions, the spectral theory, and the invertibility and completion of invertibility etc. Moverover, some other works on the perturbations of spectra for operator matrices and open problems are presented.
出处
《数学进展》
CSCD
北大核心
2009年第2期129-145,共17页
Advances in Mathematics（China）
基金
国家自然科学基金(No.10562002)
高等学校博士学科点专项科研基金(No.20070126002)
内蒙古自治区自然科学基金(No.200508010103
No.200711020106).
关键词
无穷维HAMILTON算子
特征展开定理
谱理论
可逆性
谱扰动
infinite dimensional Hamiltonian operator
expansion theorem
spectral theory
invertibility
perturbation of spectrum
