切片正则函数的一个局部柯西积分公式

Pub Date : 2023-05-30 DOI:10.1007/s40315-023-00485-5

Alessandro Perotti

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引用次数: 2

摘要

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。

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A Local Cauchy Integral Formula for Slice-Regular Functions

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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