扰动双参数C_0半群的范数连续性和直接紧性  

Norm Continuity and Immediate Compactness of Perturbed Two-paramter C_0 Semgroups

作　　者：宋学力[1] 代辉亚[2,3] 彭济根[3] 

机构地区：[1]长安大学理学院,陕西西安710064 [2]河南工业大学理学院,河南郑州450001 [3]西安交通大学数学与统计学院,陕西西安710049

出　　处：《数学的实践与认识》2013年第21期222-226,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11201038;11131006);陕西省自然科学基金(2011JQ1004);长安大学中央高校基本科研业务费专项资金资助项目(2013G2121017;CHD2012TD015)

摘　　要：双参数半群已经被成功地应用于研究具有多维参数的Markov过程.在双参数C_0半群被有界扰动之后仍然是一个双参数C_0半群的基础上,首先讨论扰动半群和原半群的大小关系;其次,利用获得的扰动结果,证明扰动双参数半群分别继承原半群的范数连续性和直接紧性.获得的结果是单参数C_0半群相应结论的推广.Two-parameter semigroups have been successfully applied to research Markov process with several dimensional parameters. Based on the fact that the bounded perturbation of a two-parameter Co semigroup still generates a two-parameter Co one, the paper firstly discusses the relation between the perturbed semigroup and the original semigroup. Secondly, we prove that the perturbed semigroup persists the norm continuity and immediate compactness of the original semigroup by the perturbed result obtained, respectively. Our results are the extension of the responding ones of one parameter Co semigroup.

关 键 词：双参数CO半群 有界扰动 范数连续性 直接紧性 

分 类 号：O152.7[理学—数学]