四元Heisenberg群上次拉普拉斯算子的m幂次的基本解

王海蒙, 周璇, 赵玉娟

数学学报 ›› 2020, Vol. 63 ›› Issue (3) : 229-244.

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数学学报 ›› 2020, Vol. 63 ›› Issue (3) : 229-244. DOI: 10.12386/A2020sxxb0019
论文

四元Heisenberg群上次拉普拉斯算子的m幂次的基本解

    王海蒙, 周璇, 赵玉娟
作者信息 +

The Fundamental Solution for the m-th Powers of the sub-Laplacian on the Quaternionic Heisenberg Group

    Hai Meng WANG, Xuan ZHOU, Yu Juan ZHAO
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文章历史 +

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.

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.

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

Key words

quaternionic Heisenberg group / group Fourier transform / Sub-Laplacian / Plancherel formula / fundamental solution

引用本文

导出引用
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. 数学学报, 2020, 63(3): 229-244 https://doi.org/10.12386/A2020sxxb0019
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. Acta Mathematica Sinica, Chinese Series, 2020, 63(3): 229-244 https://doi.org/10.12386/A2020sxxb0019

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基金

江苏省高校自然科学基金面上项目(18KJD0004)

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