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| A CONSTRUCTIVE PROOF OF THE INVERSION FORMULA FOR ZONAL FUNCTIONS ON SL(2,R） |
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Citation： |
Xiao Changbai,Zheng Weixing,Su Weiyi.A CONSTRUCTIVE PROOF OF THE INVERSION FORMULA FOR ZONAL FUNCTIONS ON SL(2,R）[J].Chinese Annals of Mathematics B,1996,17(1):81~88 |
| Page view： 1083
Net amount： 732 |
Authors： |
Xiao Changbai; Zheng Weixing;Su Weiyi |
Foundation： |
Project supported by the National Natural Science
Foundation of China |
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| Abstract： |
A constructive proof is given for the inversion formula for zonal functions
on $ SL(2,R).$ A concretely constructed sequence of zonal functions
are proved to satisfy the inversion formula obtained by Harish-Chandra for
compact supported infinitely differentiable zonal functions. Making use
of the property of this sequence somehow similar to that of approximation
kernels, the authors deduce that the inversion formula is true for continuous zonal
functions on $ SL(2,R)$ under some condition. The classical result can
be viewed as a corollary of the results here. |
Keywords： |
Inversion formula, Zonal function,
Approximation kernel |
Classification： |
43A80, 22E30 |
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