We prove the completeness in L₂(D) of the family of all pairwise products of solutions to the Helmholtz equation that are regular in a bounded domain D ⊂ ℝ³ and fundamental solutions to this equation with singularities at points located on the straight line \({\cal L} \subset {ℝ^3},\overline D \cap {\cal L} = \emptyset \).

中文翻译：

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关于亥姆霍兹方程解的乘积的完备性

我们证明完整性大号₂（d家庭的亥姆霍兹方程在有界域常规解决方案的所有成对产品）d ⊂ℝ ³和这个方程与位于直线点奇异基本解\ （{\ cal L} \ subset {ℝ^ 3}，\ overline D \ cap {\ cal L} = \ emptyset \）。