Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations
Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations
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DOI：
10.1137/0916051
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发表时间：
1995-07
期刊：
影响因子：
--
通讯作者：
M. Epton;B. Dembart
中科院分区：
文献类型：
--
作者：
M. Epton;B. Dembart
总结和推广了三维拉普拉斯方程和亥姆霍兹方程的多极平移算符的数学理论。拉普拉斯方程的新结果包括内到内平移定理的初等证明，由此得到了类似于Helmholtz方程的远场签名函数的定义。Helmholtz方程的理论是通过平移算符的一种新的卷积形式发展起来的，它通过Wigner 3-j符号与Rokhlin的对角形式相联系。
The mathematical theory of multipole translation operators for the three-dimensional Laplace and Helmholtz equations is summarized and extended. New results for the Laplace equation include an elementary proof of the inner-to-inner translation theorem, from which follows the definition of a far-field signature function analogous to that of the Helmholtz equation. The theory for the Helmholtz equation is developed in terms of a new convolutional form of the translation operator, which is connected to Rokhlin’s diagonal form by means of Wigner 3-j symbols.