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2010•Journal of MathematicsRequires access

CAUCHY INTEGRAL FORMULA AND CAUCHY-POMPEIU FORMULA ON UNBOUNDED DOMAINS IN UNIVERSAL CLIFFORD ANALYSIS

Na Xu, Jinyuan Du

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Abstract

In this article,we study the Cauchy integral formula and Cauchy-Pompeiu formula in universal Clifford analysis.By introducing the modified Cauchy kernel,we obtain the two formulas for functions with values in a universal Clifford algebra on unbounded domains.They are the extension of the results on bounded domains and lay a strong foundation for studying the boundary value problem on unbounded domains.

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In this article,we study the Cauchy integral formula and Cauchy-Pompeiu formula in universal Clifford analysis.By introducing the modified Cauchy kernel,we obtain the two formulas for functions with values in a universal Clifford algebra on unbounded domains.They are the extension of the results on bounded domains and lay a strong foundation for studying the boundary value problem on unbounded domains.

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Available abstract

In this article,we study the Cauchy integral formula and Cauchy-Pompeiu formula in universal Clifford analysis.By introducing the modified Cauchy kernel,we obtain the two formulas for functions with values in a universal Clifford algebra on unbounded domains.They are the extension of the results on bounded domains and lay a strong foundation for studying the boundary value problem on unbounded domains.

Key concepts: Mathematics, Clifford analysis, Cauchy's integral formula, Cauchy distribution, Cauchy's integral theorem, Bounded function, Pure mathematics, Cauchy boundary condition

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CAUCHY INTEGRAL FORMULA AND CAUCHY-POMPEIU FORMULA ON UNBOUNDED DOMAINS IN UNIVERSAL CLIFFORD ANALYSIS — Research Paper | ScholarLens