两类Hamilton算子族广义本征函数系的完备性  

Completeness of Generalized Eigenfunction System of Two Types of Hamiltonian Operator Family

作　　者：齐春宇 侯国林[1] 阿拉坦仓 QI Chunyu;HOU Guolin;Alatancang(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;Mathematics Science College,Inner Mongolia Normal University,Hohhot 010022,China)

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：《内蒙古大学学报（自然科学版）》2021年第2期113-117,共5页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金(11861048);高等学校青年科技英才计划项目(NJYT-15-B03);内蒙古自治区自然科学基金(2016MS0105);内蒙古自治区“草原英才”工程青年创新人才项目(1300020608)。

摘　　要：对源于力学的板弯曲问题,导出了两类Hamilton系统,进而导出了两类无界Hamilton算子族,研究了这两类广义本征函数系的性质,证明了广义本征函数系在Cauchy主值意义下的完备性。最后给出了两类Hamilton系统的一般解,并探讨了解的相容性。The two kinds of Hamiltonian systems are derived for the plate bending problem arising from the elasticity.And two kinds of Hamiltonian operators are obtained.Moreover, the completeness of its generalized eigenfunction systems are proved in the sense of Cauchy principle value.Finally, the general solutions of the two kinds of Hamiltonian systems are given and their compatibility are discussed.

关 键 词：Hamilton算子族 正交关系 CAUCHY主值 完备性 

分 类 号：O175.3[理学—数学]