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A nonlinear problem on mean-square approximation of a real finite nonnegative continuous function with respect to two variables by the module of double Fourier integral dependent on two parameters is investigated. Finding the optimum solutions (prototypes of Fourier integral) is reduced to investigation and numerical solution of Hammerstein type nonlinear two-dimensional integral equation. Algorithms for numerical finding the lines of branching and branching-off solutions to this equation are constructed and justified. Numerical examples are given.

nonlinear spectral problem; continuous components of spectrum; holomorphic operator-function; implicit function method