In this paper, we review the notion of generalized partial-slice monogenic functions that was introduced by the authors in Xu and Sabadini (Generalized partial-slice monogenic functions, arXiv:2309.03698, 2023). The class of these functions includes both the theory of monogenic functions and of slice monogenic functions over Clifford algebras and it is obtained via a synthesis operator which combines a generalized Cauchy–Riemann operator with an operator acting on slices. Besides recalling the fundamental features, we provide a notion of \(*\)-product based on the CK-extension and discuss the smoothness of generalized partial-slice functions.

在本文中，我们回顾了 Xu 和 Sabadini 的作者引入的广义部分切片单基因函数的概念（广义部分切片单基因函数，arXiv：2309.03698，2023）。这些函数的类别包括单基因函数理论和 Clifford 代数上的切片单基因函数理论，并且它是通过综合算子获得的，该综合算子将广义柯西-黎曼算子与作用于切片的算子相结合。除了回顾基本特征之外，我们还提供了基于 CK 扩展的\(*\) -乘积的概念，并讨论了广义部分切片函数的平滑性。