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2003•Unpublished venueRequires access

On higher order Cauchy-Pompeiu formula in Cliord analysis and its applications

Heinrich Begehr, Jinyuan Du, Zhongxiang Zhang

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Abstract

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 [2]. As applications we give the mean value theorem and as special case the higher order Cauchy’s integral formula. 2000 Mathematical Subject Classification: 35C10, 31B05, 30G35.

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What this paper is about

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 [2]. As applications we give the mean value theorem and as special case the higher order Cauchy’s integral formula. 2000 Mathematical Subject Classification: 35C10, 31B05, 30G35.

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OpenAlex reports 18 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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 [2]. As applications we give the mean value theorem and as special case the higher order Cauchy’s integral formula. 2000 Mathematical Subject Classification: 35C10, 31B05, 30G35.

Key concepts: Mathematics, Cauchy distribution, Cauchy's integral formula, Clifford analysis, Kernel (algebra), Order (exchange), Clifford algebra, Pure mathematics

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