Cauchy Integral Formula on the Distinguished Boundary with Values in Complex Universal Clifford Algebra

As an integral representation for holomorphic functions, Cauchy integral formula plays a significant role in the function theory of one complex variable and several complex variables. In this paper, using the idea of several complex analysis we construct the Cauchy kernel in universal Clifford analy...

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Bibliographic Details
Published in:Advances in applied Clifford algebras 2021-11, Vol.31 (5), Article 72
Main Authors: Xu, Na, Li, Zunfeng, Yang, Heju
Format: Article
Language:English
Subjects:
Analytic functions
Applications of Mathematics
Boundary value problems
Cauchy integral formula
Complex variables
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Theoretical
Vectors (mathematics)
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Summary:As an integral representation for holomorphic functions, Cauchy integral formula plays a significant role in the function theory of one complex variable and several complex variables. In this paper, using the idea of several complex analysis we construct the Cauchy kernel in universal Clifford analysis, which has generalized complex differential forms with universal Clifford basic vectors. We establish Cauchy–Pompeiu formula and Cauchy integral formula on the distinguished boundary with values in universal Clifford algebra. This work is the basis for studying the Cauchy-type integral and its boundary value problem in complex universal Clifford analysis.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-021-01175-y