无穷维Hamilton算子谱理论研究综述  

A Review for Research in Spectral Theory ofInfinite Dimensional Hamiltonian Operators

作　　者：阿拉坦仓 吴德玉[2] Alatancang;WU De-yu(Mathematics Science College,Inner Mongolia Normal University,Hohhot 010022,China;School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《内蒙古师范大学学报（自然科学版）》2021年第1期1-6,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11761029);内蒙古自治区自然科学基金资助项目(2019MS01019)。

摘　　要：对无穷维Hamilton算子谱理论研究成果进行了梳理,包括无穷维Hamilton算子辛自伴性、无穷维Hamilton算子特征函数系的完备性,以及无穷维Hamilton算子数值域等方面的研究现状和展望。提出一些关于无穷维Hamilton算子谱理论方面有待解决的问题。The research scholars and their achievements in spectral theory of infinite dimensional Hamiltonian operator were retrospected in this paper.The research status in symplectic self-adjointness of infinite dimensional Hamiltonian operator,completeness of eigenfunctions systems and numerical range of infinite dimensional Hamiltonian operator were involved.In addition,some open problems about infinite dimensional Hamiltonian operator were proposed in the paper.

关 键 词：无穷维HAMILTON算子 自伴性 数值域 完备性 

分 类 号：O175.3[理学—基础数学]