A Local Cauchy Integral Formula for Slice-Regular Functions

IF 0.6 4区数学 Q3 MATHEMATICS

Computational Methods and Function Theory Pub Date : 2023-05-30 DOI:10.1007/s40315-023-00485-5

Alessandro Perotti

引用次数: 2

Abstract

Abstract We prove a local Cauchy-type integral formula for slice-regular functions. The formula is obtained as a corollary of a general integral representation formula where the integration is performed on the boundary of an open subset of the quaternionic space, with no requirement of axial symmetry. As a step towards the proof, we provide a decomposition of a slice-regular function as a combination of two axially monogenic functions.

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切片正则函数的一个局部柯西积分公式

摘要证明了切片正则函数的一个局部柯西型积分公式。该公式作为一般积分表示公式的推论得到，其中积分在四元数空间的开放子集的边界上进行，不要求轴对称。作为证明的一步，我们提供了一个分解的切片正则函数作为两个轴向单基因函数的组合。

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

Computational Methods and Function Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.