| 关于广义Sublaplacian算子特征函数的展开 |
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| 引用本文： | 张震球,束立生.关于广义Sublaplacian算子特征函数的展开[J].数学学报,1996,39(1):102-107. |
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| 作者姓名： | 张震球 束立生 |
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| 作者单位： | 天津大学数学系!天津300072(张震球)，安徽师范大学数学系!芜湖241000(束立生) |
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| 摘 要： | 本文研究了广义Ｓｕｂｌａｐｌａｃｉａｎ算子特征函数的展开．通过定义广义 －扭曲卷积，我们得到相应的Ｐｌａｎｃｈｅｒｅｌ定理及Ｈａｕｓｄｏｒｆｆ－Ｙｏｕｎｇ不等式，最后，我们还给出了当广义Ｓｕｂｌａｐｌａｃｉａｎ算子的特征值为离散时的一些结果．
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| 关 键 词： | 特征函数展开 扭曲卷积 限制算子 |
| 收稿时间： | 1993-12-3 |
| 修稿时间： | 1994-11-14 |
On the Eigenfunction Expansions for the Generalized Sublaplacian |
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| Zhang Zhenqiu.On the Eigenfunction Expansions for the Generalized Sublaplacian[J].Acta Mathematica Sinica,1996,39(1):102-107. |
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| Authors: | Zhang Zhenqiu |
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| Institution: | Zhang Zhenqiu (Department of Mathematics,Tianjin University,Tianjin 300072, China) Shu Lisheng (Department of Mathematics,Anhui Normal University, Wuhu 241000, China) |
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| Abstract: | In this paper, we investigate the eigenfunction expansions for the generalized Sublaplacian.By introducing the generalized -twisted convolutions, we obtain the Plancherel theorem and a Hausdorff-Young inequality. Some results are given under the condition that the eigenvalues of the generalized Sublaplacian are discrete. |
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| Keywords: | eigenfunction expansions twisted convolutions restriction operator |
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