半群上条件正定函数的扩张  

DILATIONS OF CONDITIONAL POSITIVE DEFINITE FUNCTIONS ON SEMI-GROUPS

作　　者：杨海涛[1] 

机构地区：[1]厦门理工学院数理系,厦门361003

出　　处：《系统科学与数学》2007年第5期714-719,共6页Journal of Systems Science and Mathematical Sciences

基　　金：福建省自然科学基金计划项目(2007J0193);福建省教育厅科技项目(JA06061);厦门理工学院科研项目(YKJ06004R).

摘　　要：讨论半群上条件正定函数的扩张问题.得到一个扩张定理.作为应用,得到有界扩张定理和Pontryagin空间上量子力学的一个基本定理.In this paper, problems of dilations of conditional positive definite functions on semi-groups are studied, and a dilation theorem on conditional positive definite functions on semi-groups are obtained. As applications, dilation and bounded dilation of conditional positive definite functions on semi-groups are studied. Finally a fundamental theorem for quantum mechanics on Pontryagin space is proved.

关 键 词：条件正定型 扩张 Pontryagin空间 

分 类 号：O152.7[理学—数学]