On the Completeness of Products of Solutions to the Helmholtz Equation

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 $${\cal L} \subset {ℝ^3},\overline D \cap {\cal L} = \emptyset $$ .