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Cauchy integral formula on the distinguished boundary with values in complex universal Clifford algebra. (English) Zbl 1476.30164

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.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
30E25 Boundary value problems in the complex plane
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