| Generalized Integral Representations for Functions with Values in C（V_（3,3）） |
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| 引用本文： | Klaus G¨ URLEBECK,Zhongxiang ZHANG.Generalized Integral Representations for Functions with Values in C（V_（3,3））[J].数学年刊B辑(英文版),2011,32(1):123-138. |
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| 作者姓名： | Klaus G¨ URLEBECK Zhongxiang ZHANG |
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| 作者单位： | Institut;f.Mathematik/Physik;Bauhaus-Universitt;Weimar;Coudraystr.13;D-99423;Germany; |
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| 基金项目： | Project supported by Deutscher Akademischer Austausch Dienst (German Academic Exchange Service); the National Natural Science Foundation of China (No.10471107) |
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| 摘 要： | By using the solution to the Helmholtz equation u-λu = 0(λ ≥ 0),the explicit forms of the so-called kernel functions and the higher order kernel functions are given.Then by the generalized Stokes formula,the integral representation formulas related with the Helmholtz operator for functions with values in C(V3,3) are obtained.As application of the integral representations,the maximum modulus theorem for function u which satisfies Hu = 0 is given.
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| 关 键 词： | 积分表示 Helmholtz方程 广义 Stokes公式 亥姆霍兹算子 最大模定理 核函数 显式形式 |
Generalized Integral Representations for Functions with Values in $C(V_{3,3})$ |
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| Klaus?Gürlebeck,Zhongxiang?Zhang.Generalized Integral Representations for Functions with Values in $C(V_{3,3})$[J].Chinese Annals of Mathematics,Series B,2011,32(1):123-138. |
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| Authors: | Klaus Gürlebeck Zhongxiang Zhang |
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| Institution: | 1. Institut f.Mathematik/Physik,Bauhaus-Universit(a)t Weimar,Coudraystr.13,D-99423 Weinar,Germany.
2. Corresponding author. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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| Abstract: | By using the solution to the Helmholtz equation Δu − λu = 0 (λ ≥ 0), the explicit forms of the so-called kernel functions and the higher order kernel functions are given. Then by the generalized
Stokes formula, the integral representation formulas related with the Helmholtz operator for functions with values in C(V
3,3) are obtained. As application of the integral representations, the maximum modulus theorem for function u which satisfies H
u = 0 is given. |
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| Keywords: | Universal Clifford algebra Helmholtz equation Generalized CauchyPompeiu formula |
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