Generalized Partial-Slice Monogenic Functions: A Synthesis of Two Function Theories

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2024-03-09 DOI:10.1007/s00006-024-01314-1

Zhenghua Xu, Irene Sabadini

引用次数: 0

Abstract

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.

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广义部分片单原函数：两种函数理论的合成

在本文中，我们回顾了作者在徐和萨巴迪尼（Generalized partial-slice monogenic functions, arXiv:2309.03698, 2023）一文中提出的广义部分片单生函数的概念。这类函数既包括单原函数理论，也包括克利福德代数上的切片单原函数理论，它是通过一个综合算子得到的，该算子结合了广义考奇-黎曼算子和作用于切片的算子。除了回顾基本特征之外，我们还提供了一个基于 CK 扩展的 \(*\)-product 概念，并讨论了广义部分切片函数的平滑性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.