| 四元Heisenberg群上次拉普拉斯算子的m幂次的基本解 |
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| 引用本文： | 王海蒙,周璇,赵玉娟.四元Heisenberg群上次拉普拉斯算子的m幂次的基本解[J].数学学报,2020(3):229-244. |
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| 作者姓名： | 王海蒙 周璇 赵玉娟 |
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| 作者单位： | 江苏第二师范学院数学与信息技术学院 |
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| 基金项目： | 江苏省高校自然科学基金面上项目(18KJD0004)。 |
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| 摘 要： | 本文研究了四元Heisenberg群上次拉普拉斯算子的m幂次的基本解,该结论是Heisenberg群上结果的推广.本文利用了四元Heisenberg群上的Fourier变换理论构造了该群上次拉普拉斯算子的m幂次的基本解,并且给出了基本解的积分表示.
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| 关 键 词： | 四元Heisenberg群 群上的Fourier变换 次拉普拉斯算子 Plancherel公式 基本解 |
The Fundamental Solution for the m-th Powers of the sub-Laplacian on the Quaternionic Heisenberg Group |
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| Hai Meng WANG,Xuan ZHOU,Yu Juan ZHAO.The Fundamental Solution for the m-th Powers of the sub-Laplacian on the Quaternionic Heisenberg Group[J].Acta Mathematica Sinica,2020(3):229-244. |
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| Authors: | Hai Meng WANG Xuan ZHOU Yu Juan ZHAO |
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| Institution: | (Department of Mathematics and Information Technology,Jiangsu Second Normal University,Nanjing 210013,P.R.China) |
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| Abstract: | We discuss the fundamental solution for m-th powers of the sub-Laplacian on the quaternionic Heisenberg group,This result is the extension of the conclusion on the Heisenberg group.We use the representation theory of nilpotent Lie groups of step two to analyze the associated m-th powers of the sub-Laplacian on the quaternionic Heisenberg group and to construct its fundamental solution. |
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| Keywords: | quaternionic Heisenberg group group Fourier transform Sub-Laplacian Plancherel formula fundamental solution |
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