CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS*

doi:10.1007/s10473-024-0120-4

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (1): 369-385.doi: 10.1007/s10473-024-0120-4

CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS^*

Nanbin CAO¹, Zunfeng LI^2,†, Heju YANG², Yuying QIAO³

1. School of Mathematics and Science, Hebei GEO University, Shijiazhuang 050031, China;
2. College of Science, Hebei University of Science and Technology, Shijiazhuang 050018, China;
3. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China

收稿日期:2022-08-04 修回日期:2023-07-22 出版日期:2024-02-25 发布日期:2024-02-27
通讯作者: † Zunfeng LI, E-mail: zunfeng928@163.com; Yuying QIAO, E-mail: yuyingqiao@163.com
作者简介:Nanbin CAO, E-mail: caonanbin@163.com; Heju YANG, E-mail: earnestqin@163.com
基金资助:
NSF of Hebei Province (A2022208007), the NSF of China (11571089, 11871191), the NSF of Henan Province (222300420397).

CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS^*

Nanbin CAO¹, Zunfeng LI^2,†, Heju YANG², Yuying QIAO³

1. School of Mathematics and Science, Hebei GEO University, Shijiazhuang 050031, China;
2. College of Science, Hebei University of Science and Technology, Shijiazhuang 050018, China;
3. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China

Received:2022-08-04 Revised:2023-07-22 Online:2024-02-25 Published:2024-02-27
Contact: † Zunfeng LI, E-mail: zunfeng928@163.com; Yuying QIAO, E-mail: yuyingqiao@163.com
About author:Nanbin CAO, E-mail: caonanbin@163.com; Heju YANG, E-mail: earnestqin@163.com
Supported by:
NSF of Hebei Province (A2022208007), the NSF of China (11571089, 11871191), the NSF of Henan Province (222300420397).

摘要/Abstract

摘要： Clifford analysis is an important branch of modern analysis; it has a very important theoretical significance and application value, and its conclusions can be applied to the Maxwell equation, Yang-Mill field theory, quantum mechanics and value problems. In this paper, we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis, and get the Plemelj formula for it. Second, we discuss the Hölder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra. Finally, we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.

关键词: Clifford analysis, Cauchy type integral, Plemelj formula, Hölder continuous;, boundary value problems

Abstract: Clifford analysis is an important branch of modern analysis; it has a very important theoretical significance and application value, and its conclusions can be applied to the Maxwell equation, Yang-Mill field theory, quantum mechanics and value problems. In this paper, we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis, and get the Plemelj formula for it. Second, we discuss the Hölder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra. Finally, we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.

Key words: Clifford analysis, Cauchy type integral, Plemelj formula, Hölder continuous;, boundary value problems

中图分类号:

32A30

Nanbin CAO, Zunfeng LI, Heju YANG, Yuying QIAO. CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS^*[J]. 数学物理学报(英文版), 2024, 44(1): 369-385.

Nanbin CAO, Zunfeng LI, Heju YANG, Yuying QIAO. CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS^*[J]. Acta mathematica scientia,Series B, 2024, 44(1): 369-385.

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CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS^*

CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS^*

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