一类无界算子矩阵根子空间的完备性  

Completeness for root vectors system of a class of unbounded operator matrices

作　　者：吴德玉[1] 阿拉坦仓[2] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]呼和浩特民族学院,呼和浩特010050

出　　处：《中国科学：数学》2016年第4期439-450,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11371185);内蒙古自然科学基金(批准号:2013ZD01);国家留学基金(批准号:201308155047)资助项目

摘　　要：本文研究了在弹性力学和线性Hamilton系统中出现的一类无界算子的性质,给出了这类算子的根向量组在Hilbert空间中Cauchy主值意义下完备的充分条件.最后,以板弯曲方程为例讨论了系统对应的算子根向量组的完备性并加以说明判别准则的有效性.In this paper, a class of unbounded operators that appear naturally in the study of elasticity and infinite dimensional linear Hamiltonian systems are studied, and the conditions under which the root vectors for operators from this class is complete in a Hilbert space under the sense of Cauchy principal value are obtained.In the end, as applications we consider the corresponding infinite dimensional Hamiltonian operator of a class of plate bending equations, and the completeness for root vectors system are proved.

关 键 词：根向量 Cauchy主值意义 完备性 无穷维HAMILTON算子 

分 类 号：O177[理学—数学]