Scalar products for the regular analytic vectors of the Laplace operator in the solenoidal subspace

The Laplace operator on the subspace of solenoidal vector functions of three variables vanishing with the first derivatives in the selected points $ \vec{x_{n}} $, $ n=1,\ldots, N $ is a symmetric operator with deficiency indices (3N,3N). The calculation of the scalar products of its regular analytic vectors is the central point in the construction of the resolvents of its selfadjoint extensions by means of the Kreins formula.