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On higher order Cauchy-Pompeiu formula in Clifford analysis and its applications. (English) Zbl 1249.35040
Summary: In this paper, we firstly construct the kernel functions which are necessary for us to study universal Clifford analysis. Then we obtain the higher order Cauchy-Pompeiu formulas for functions with values in a universal Clifford algebra, which are different from those in [Z. Anal. Anwend. 18, No. 2, 361–377 (1999; Zbl 0940.31005)]. As applications we give the mean value theorem and as special case the higher order Cauchy’s integral formula.

MSC:
35C10 Series solutions to PDEs
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
30G35 Functions of hypercomplex variables and generalized variables
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