加权次致函数的B-P公式和Cauchy积分公式\(\dag \)

IF 1.2 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2025-08-14 DOI:10.1007/s00006-025-01405-7

Ying Li, Liping Wang, Xin Jiang, Xiaojia Yang

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引用次数: 0

摘要

为了研究加权次致函数的B-P公式，首先给出了两个重要的引理，它们解决了Clifford值函数在乘法运算中不可交换的困难。然后，利用上述引理的结论，结合非欧几里得距离下\(\textrm{d}\sigma \)与欧几里得距离下\(\textrm{d}\mu _{r}\)的关系，通过挖掘满足Stokes公式使用条件的奇异点，并引入新的算子简化计算步骤，得到加权次源函数的B-P公式。进一步得到了加权次致函数的柯西积分公式。

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The B–P Formula and Cauchy Integral Formula for Weighted Inframonogenic Functions\(\dag \)

In this paper, in order to study the B–P formula of weighted inframonogenic functions, two important lemmas are first given, which solve the difficulty caused by the non commutativity of Clifford valued functions in multiplication operations. Then, using the conclusion of the above lemmas and the relationship between \(\textrm{d}\sigma \) under non-Euclidean distances and \(\textrm{d}\mu _{r}\) under Euclidean distances, the B–P formula for weighted inframonogenic functions is obtained by digging out singularities to satisfy the conditions for using the Stokes formula, and introducing new operators to simplify the calculation steps. Furthermore, the Cauchy integral formula for weighted inframonogenic functions is obtained.

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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.