ABSTRACT

We use the representation theory of nilpotent Lie groups of step two to find the fundamental solution for the Paneitz operator on the anisotropic quaternionic Heisenberg group. For the isotropic case, we also construct the closed-form of this solution. This result is the extension of the conclusion on the Heisenberg group.

中文翻译：

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各向异性四元数海森堡群的 Paneitz 算子

摘要

我们使用第二步的幂零李群的表示理论来找到各向异性四元数海森堡群上的 Paneitz 算子的基本解。对于各向同性的情况，我们还构造了该解的封闭形式。这个结果是对海森堡群结论的延伸。