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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.

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