The Laurent expansion and residue theorem of weighted monogenic functions

IF 0.6 4区数学 Q3 MATHEMATICS

Complex Variables and Elliptic Equations Pub Date : 2023-10-01 DOI:10.1080/17476933.2023.2260995

Liping Wang, Liping Luo, Ying Li, Xin Jiang

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引用次数: 0

Abstract

ABSTRACTFirstly, the definition of p order homogeneous weighted right monogenic polynomials is given, and the hypercomplex variables are introduced in order to construct a basis of all homogeneous weighted right monogenic polynomials of degree p, then the second Taylor expansion of the weighted right monogenic functions is obtained. Secondly, the weighted left monogenic functions are constructed from continuous functions in different regions, and corresponding Taylor expansions are given. Finally, on the basis of the previous conclusions, the Laurent expansion and residue theorem of the weighted left monogenic functions are proved.KEYWORDS: Weighted monogenic functionsp order homogeneous weighted right monogenic polynomialshypercomplex variablesLaurent expansionresidue theoremAMS SUBJECT CLASSIFICATIONS: 30B1030G3532A05 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by the Natural Science Foundation of Hebei Province [grant numbers A2020205008 and A2015205012], Key Foundation of Hebei Normal University [grant number L2021Z01] and the National Natural Science Foundation of China [grant numbers 11401162, 11871191, and 11571089].

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加权单基因函数的劳伦展开式和残数定理

摘要首先给出了p阶齐次加权右单核多项式的定义，引入超复变量，构造了p阶所有齐次加权右单核多项式的基，得到了加权右单核函数的第二次泰勒展开式。其次，从不同区域的连续函数构造加权左单基因函数，并给出相应的泰勒展开式;最后，在前面结论的基础上，证明了加权左单基因函数的劳伦展开式和剩余定理。关键词:加权单基因函数;序齐次加权右单基因多项式;超复变量;laurent可扩张残数定理;课题分类:30B1030G3532A05披露声明作者未报告潜在利益冲突。项目资助:河北省自然科学基金项目[批准号:A2020205008和A2015205012]、河北师范大学重点基金项目[批准号:L2021Z01]、国家自然科学基金项目[批准号:114001162、11871191和11571089]。

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来源期刊

Complex Variables and Elliptic Equations MATHEMATICS-

CiteScore

2.00

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： Complex Variables and Elliptic Equations is devoted to complex variables and elliptic equations including linear and nonlinear equations and systems, function theoretical methods and applications, functional analytic, topological and variational methods, spectral theory, sub-elliptic and hypoelliptic equations, multivariable complex analysis and analysis on Lie groups, homogeneous spaces and CR-manifolds. The Journal was formally published as Complex Variables Theory and Application.