一类无穷维Hamilton算子特征函数系的完备性  

Completeness for the Eigenfunction System of a Class of Infinite Dimensional Hamiltonian Operators

作　　者：黄俊杰[1] 阿拉坦仓[1] 陈阿茹娜[2] 

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

出　　处：《应用数学学报》2008年第3期457-466,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10562002);内蒙古自治区自然科学基金(200508010103，200711020106);内蒙古大学高层次引进人才科研启动基金(206029)资助项目．

摘　　要：本文对分离变量后可转化为Sturm-Liouville问题的偏微分方程,引入Hamilton体系,从而导出无穷维Hamilton算子的特征值问题.然后利用辛空间的知识讨论了无穷维Hamilton算子特征函数系的完备性,为对此类方程应用基于Hamilton体系的分离变量法提供了理论基础.作为应用,还给出了波动方程导出的无穷维Hamilton算子特征函数系的完备性.For the equations that lead to Sturm-Liouville problem through separating variables, the present paper introduces Hamiltonian systems, which derives to the eigenvalue problem of infinite dimensional Hamiltonian operators. Then, the completeness of the eigenfunction system of the operators is investigated by using the knowledge of symplectic spaces, which lays the theoretical foundation for employing the method of separation of variables based on Hamiltonian systems. As an application, the completeness of the eigenfunction system of the infinite dimensional Hamiltonian operator corresponding to a wave equation is given.

关 键 词：无穷维HAMILTON系统 无穷维HAMILTON算子 特征值问题 特征函数系 完备性 

分 类 号：O175.3[理学—数学] O175.9[理学—基础数学]