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

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

Nanbin CAO1, Zunfeng LI2,†, Heju YANG2, Yuying QIAO3   

  1. 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 LI2,†, Heju YANG2, Yuying QIAO3   

  1. 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: 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