Hamilton算子矩阵的半群生成性质  

Semigroup generation properties of Hamiltonian operator matrices

作　　者：刘杰[1,2] 黄俊杰[1] 阿拉坦仓[1,3] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古大学满洲里学院,满洲里021400 [3]呼和浩特民族学院,呼和浩特010051

出　　处：《中国科学：数学》2015年第4期373-380,共8页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11461049和11371185);内蒙古自然科学基金(批准号:2013JQ01和2013ZD01)资助项目

摘　　要：本文研究Hamilton算子矩阵生成压缩半群的问题,采用对角元算子的耗散性刻画整个算子的耗散性,借助空间分解和二次补描述右半实轴包含于整体算子的预解集,进而给出若干半群生成的充分必要条件.This paper deals with the problem for Hamiltonian operator matrices to generate contraction semigroups. The dissipativity of the operator matrix is characterized by those of its diagonal entries. By means of space decomposition and quadratic complements, it is described that the right real axis is contained in the resolvent set of the operator matrix. Based on these properties, some necessary and sufficient conditions on semigroup generation are further given.

关 键 词：Hamilton算子矩阵 压缩半群 数值域 二次补 空间分解 

分 类 号：O151.21[理学—数学] O152.7[理学—基础数学]