数学物理学报(英文版)

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HOLOMORPHIC HARMONIC ANALYSIS ON COMPLEX REDUCTIVE GROUPS

安金鹏; 钱敏; 王正栋   

  1. 北京大学数学学院, 北京 100871
  • 收稿日期:2005-12-23 修回日期:2007-03-16 出版日期:2008-07-20 发布日期:2008-07-20
  • 通讯作者: 安金鹏
  • 基金资助:

    This work is supported by the 973 Project Foundation of China (#TG1999075102)

HOLOMORPHIC HARMONIC ANALYSIS ON COMPLEX REDUCTIVE GROUPS

An Jinpeng; Qian Min; Wang Zhengdong   

  1. School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Received:2005-12-23 Revised:2007-03-16 Online:2008-07-20 Published:2008-07-20
  • Contact: An Jinpeng

摘要:

The authors define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties such as the Fourier inversion formula, and give some applications. The definition of the
holomorphic Fourier transform makes use of the notion of K-admissible measures. The authors prove that K-admissible measures are abundant, and the definition of holomorphic Fourier transform is independent of the choice of K-admissible measures.

关键词: Complex reductive group, Fourier transform, holomorphic representation

Abstract:

The authors define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties such as the Fourier inversion formula, and give some applications. The definition of the
holomorphic Fourier transform makes use of the notion of K-admissible measures. The authors prove that K-admissible measures are abundant, and the definition of holomorphic Fourier transform is independent of the choice of K-admissible measures.

Key words: Complex reductive group, Fourier transform, holomorphic representation

中图分类号: 

  • 43A30