Cauchy theorems for solutions to polynomial Dirac equations with \(\alpha \)-weight in superspace

IF 1.2 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2025-09-15 DOI:10.1007/s00006-025-01408-4

Yonghong Xie, Shuoxing He, Xiaojing Du

引用次数: 0

Abstract

In this paper, Cauchy theorems for solutions to polynomial Dirac equations with \(\alpha \)-weight in superspace are studied using two methods. First, by constructing a new fundamental solution, the first kind of Cauchy theorem is obtained. Then the connection between polynomial Dirac operators with \(\alpha \)-weight and iterative Dirac operators with \(\alpha \)-weight in superspace is obtained. Finally, using this connection, the second kind of Cauchy theorem is obtained.

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超空间中\(\alpha \) -权的多项式狄拉克方程解的柯西定理

本文用两种方法研究了超空间中\(\alpha \) -权的多项式狄拉克方程解的柯西定理。首先，通过构造一个新的基本解，得到了第一类柯西定理。然后得到了超空间中具有\(\alpha \) -权的多项式狄拉克算子与具有\(\alpha \) -权的迭代狄拉克算子之间的联系。最后，利用这一联系，得到了第二类柯西定理。

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.