四元Heisenberg群上次拉普拉斯算子的m幂次的基本解

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

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.

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.