SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS IN COMPLEX CLIFFORD ANALYSIS |
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| Authors: | Ku Min Du Jinyuan Wang Daoshun |
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| Institution: | [1]Tsinghua National Laboratory for Information Science and Technology, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China [2]School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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| Abstract: | In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of Cn+1, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation DΔmf = 0, obtain the integral representation formula for the complex holomorphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of Cn+1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them. |
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| Keywords: | Complex Clifford algebra holomorphic Cliffordian functions Taylor expansion Laurent expansion invariance |
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