On calculation of wave field of the source inside a thin sphere with a slit

A strict solution of the problem of the diffraction on a sphere with a slit is obtained. The solution is given in terms of a system of linear algebraic equations of the second kind for Fourier coefficients of the wave field. The matrix operator is compact so that it is not difficult to deduce the convergence of the reduction method. The norm of the operator is small, if the parameters of the problem are in some domain. The system is convenient for calculation.