The action of the Moisil-Theodoresco operator over a quaternionic valued function defined on \({\mathbb {R}}^3\) (sum of a scalar and a vector field) in Cartesian coordinates is generally well understood. However this is not the case for any orthogonal curvilinear coordinate system. This paper sheds some new light on the technical aspect of the subject. Moreover, we introduce a notion of quaternionic Laplace operator acting on a quaternionic valued function from which one can recover both scalar and vector Laplacians in the vector analysis context.

中文翻译：

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正交曲线坐标系中的Moisil-Theodoresco算子

众所周知，Moisil-Theodoresco算符对笛卡尔坐标中\（{\ mathbb {R}} ^ 3 \）（标量和矢量场之和）上定义的四元数值函数的作用。但是，对于任何正交曲线坐标系来说并非如此。本文为该主题的技术方面提供了一些新的思路。此外，我们引入了作用于四元数值函数的四元数Laplace算符的概念，从中可以在矢量分析环境中同时恢复标量和向量Laplacians。