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| Generalized Integral Representations for Functions with Values in $C(V_{3,3})$ |
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Citation： |
Klaus G¨ URLEBECK,Zhongxiang ZHANG.Generalized Integral Representations for Functions with Values in $C(V_{3,3})$[J].Chinese Annals of Mathematics B,2011,32(1):123~138 |
| Page view： 1732
Net amount： 1400 |
Authors： |
Klaus G¨ URLEBECK; Zhongxiang ZHANG; |
Foundation： |
the Deutscher Akademischer Austausch Dienst (German Academic Exchange Service)
and the National Natural Science Foundation of China (No. 10471107). |
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| Abstract： |
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. |
Keywords： |
Universal Clifford algebra, Helmholtz equation, Generalized Cauchy-
Pompeiu formula |
Classification： |
30G35 |
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