Inverse Transmutation Operator for \(\alpha \)-Hyperholomorphic Functions in Clifford Analysis

IF 1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2026-10-16 DOI:10.1007/s00006-026-01462-6

Doan Cong Dinh, Luong Thi Tuyet

引用次数: 0

Abstract

This paper revisits \(\alpha \)-hyperholomorphic functions in Clifford analysis, that is, functions satisfying the equation \( Du - u\alpha = 0, \) where D denotes the Dirac operator in \(\mathbb {R}^n\) and \(\alpha \in \mathbb {C}_{0,n}\). A transmutation operator for \(\alpha \)-hyperholomorphic functions has previously been constructed, mapping each monogenic function in a star-like domain to an \(\alpha \)-hyperholomorphic one. In the present work, we derive explicit integral kernels for the inverse of this operator.

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Clifford分析中\(\alpha \) -超全纯函数的逆变换算子

本文重新研究了Clifford分析中的\(\alpha \) -超全纯函数，即满足方程\( Du - u\alpha = 0, \)的函数，其中D为\(\mathbb {R}^n\)和\(\alpha \in \mathbb {C}_{0,n}\)中的Dirac算子。先前已经构造了\(\alpha \) -超全纯函数的嬗变算子，将星形区域中的每个单基因函数映射到\(\alpha \) -超全纯函数。在本工作中，我们导出了该算子逆的显式积分核。

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.