局部紧致拓扑群中的共轭比序列  

On the Conjugate Ratio Sequences in Locally Compact Groups

作　　者：郝凤歧 

机构地区：[1]应用数学系

出　　处：《清华大学学报（自然科学版）》1990年第6期102-106,共5页Journal of Tsinghua University(Science and Technology)

摘　　要：弱内自可靠群或［ＩＡ］群是一类重要的局部紧致拓扑群，是包含可靠群（当然也包含交换群，紧致群）在内的一大类拓外群。［ＩＡ］群上的调和分析已有许多进展，［ＩＡ］群的刻划，判别已成为极其重要的问题。作者曾用组合方法与集合论方法，提出共轭比序列的概念，并证明了判别［ＩＡ］群的一系列充分必要条件。在此基础上对共轭比序列的一致收敛性进行更进一步的研究，从而又获得一个［ＩＡ］群的充分条件。The weakly inner amenable groups or (IA) groups form a very important class of locally compact groups which contains amenable groups (including abelian groups and compact groups). There have been a lot of remarkable developments of harmonic analysis on (IA) groups. How to characterize and identify (IA) groups is a significant problem. The author introduced the concept of conjugate ratio sequence and proved a sequence of necessary and sufficient conditions for (IA) groups by means of combinatorics and set theory. The main purpose of this paper is to study further the uniform convergence of the conjugate ratio sequences in locally compact groups and a sufficient condition of (IA) groups is obtained as well.

关 键 词：拓扑群 局部紧致 共轭比 HAAR测度 

分 类 号：O152.4[理学—数学]