期刊论文详细信息
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 卷:296
Approximating Fourier transformation of orbital integrals
Article
Lim, CKA
关键词: Fourier transform;    Fourier inversion;    orbital integral;    Plancherel formula;    semisimple;    infinite center;    real reductive Lie group;   
DOI  :  10.1016/j.jmaa.2004.04.024
来源: Elsevier
PDF
【 摘 要 】

In this paper, we are concerned with orbital integrals on a class C of real reductive Lie groups with non-compact Iwasawa K-component. The class C contains all connected semisimple Lie groups with infinite center. We establish that any given orbital integral over general orbits with compactly supported continuous functions for a group G in C is convergent. Moreover, it is essentially the limit of corresponding orbital integrals for its quotient groups in Harish-Chandra's class. Thus the study of orbital integrals for groups in class C reduces to those of Harish-Chandra's class. The abstract theory for this limiting technique is developed in the general context of locally compact groups and linear functionals arising from orbital integrals. We point out that the abstract theory can be modified easily to include weighted orbital integrals as well. As an application of this limiting technique, we deduce the explicit Plancherel formula for any group in class C. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free   

【 预 览 】
附件列表
Files Size Format View
10_1016_j_jmaa_2004_04_024.pdf 125KB PDF download
  文献评价指标  
  下载次数:0次 浏览次数:0次