| A CONSTRUCTIVE PROOF OF THE INVERSION FORMULA FOR ZONAL FUNCTIONS ON SL(2,R） |
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| 作者姓名： | Xiao Changbai Zheng Weixing Su Weiyi |
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| 作者单位： | Department of Mathematics，Nanjing University Nanjing 210093，China. |
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| 摘 要： | 1.IntroductionLeSL(2,R)denotethemultiplicativegroupofall2x2realm8triceswithdet-nat1.InthispaPer,weuseGtodenotebothSL(2,R)andthellnearLiegroupbecausetheyareisomorphictoeachother.Forj={o,1/2},s=1 iA(whereAER,andRisthesetofallrealnumbers),letVi,8betheprincipalcolltinuousseriesofunitaryrepresentationsofG(cf.4]).SetBytheIwasawadecomposition,anygEGcanbeuniquelywhttenasg=usatnr,u8ESK,afESA,nrESN.Al8oanyginGhasaCartandecompositionasfollows:Afunctionf0nGissaidtobeazonalfunctionifitsatisf…
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| 关 键 词： | 线性函数 倒置公式 近似值 数学分析 证明方法 |
| 收稿时间： | 1993/11/18 0:00:00 |
A CONSTRUCTIVE PROOF OF THE INVERSION FORMULA FOR ZONAL FUNCTIONS ON SL(2, R) |
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| 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,Series B,1996,17(1):81-88. |
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| Authors: | Xiao Changbai Zheng Weixing and Su Weiyi |
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| Institution: | DepartmentofMathematics,NanjingUniversity,Nanjing210093,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 drictions 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 approxination 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. |
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| Keywords: | Inversion formula Zonal function Approximation kernel |
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