On Hardy's Theorem on SU(1,1)

作     者：Takeshi KAWAZOE Jianming LIU 

作者机构：Denartment of Mathematics Keio University at Fujisawa Endo FujisawaKanagawa 252-8520Japan Laboratory of Mathematics and Applied Mathematics School of Mathematical Sciences Peking UniversityBeiJing 100871China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2007年第28卷第4期

页      面：429-440页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Project supported by Grant-in-Aid for Scientific Research(C)of Japan(No.16540168) the National Natural Science Foundation of China(No.10371004) 

主　　题：Heat kernel Jacobi transform Plancherel formula 

摘      要：The classical Hardy theorem asserts that f and its Fourier transform f can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU（1, 1） there are infinitely many “good functions in the sense that f and its spherical Fourier transform y both have good decay. In this paper, we shall characterize such functions on SU（1, 1）.