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| On Hardy’s Theorem on SU(1, 1) |
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Citation： |
Takeshi KAWAZOE,Jianming LIU.On Hardy’s Theorem on SU(1, 1)[J].Chinese Annals of Mathematics B,2007,28(4):429~440 |
| Page view： 1107
Net amount： 818 |
Authors： |
Takeshi KAWAZOE; Jianming LIU |
Foundation： |
Grant-in-Aid for Scientific Research (C) of Japan (No. 16540168) and the National Natural Science Foundation of China (No. 10371004) |
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| Abstract： |
The classical Hardy theorem asserts that $f$ and its Fourier transform $\wh f$ can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on ${\rm SU}(1,1)$ there are
infinitely many ``good" functions in the sense that $f$ and its spherical Fourier transform $\wt f$ both have good decay. In this paper, we shall characterize such functions on ${\rm SU}(1,1)$. |
Keywords： |
Heat kernel, Jacobi transform, Plancherel formula |
Classification： |
22E30, 43A80, 43A90, 33C45 |
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