A boundary condition on the volume potential was demonstrated for an arbitrary domain ω. The eigenvalues and the eigen-functions of the volume potential were found for the 2 disk and the 3 ball. It was shown in the Poisson equation that self adjoint differential operators were generated by boundary conditions. One of the main results of the investigation gave boundary conditions uniquely determining the volume potential. The first theorem stated that the spectral problem on the eigenvalues of the volume potential on the disk was equivalent to the spectral problem.
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