Simple and double layer potentials in the Hilbert spaces

The boundary value problem for the Laplacian has numerous applications at the solution of the many applied problems of electrophysics. The Hilbert spaces elements of which can be represented as the sum of simple and double layer potentials are considered in this article. We prove that these spaces are orthogonal relatively the introduced scalar product and the elements of its union can be single-valuedly represented as a sum of above-mentioned potentials. Obtained results allow to formulate the independent classes of the boundary value problems for Laplacian in R/sup 3/ in these Hilbert spaces, to use the potential theory methods for its solution and to obtain the proof of well-posed solution for both boundary value problems and equivalent to the integral equations including the equations of the first kind.