On the best mean-square approximation of a real nonnegative finite continuous function of two variables by the modulus of a double Fourier integral. I

We study the nonlinear problem of mean-square approximation of a real finite nonnegative continuous function of two variables by the modulus of a double Fourier integral depending on two parameters. The solution of this problem is reduced to the solution of a nonlinear two-dimensional integral equation of the Hammerstein type. Numerical algorithms for determination of branching lines and branched solutions of equation are constructed and substantiated. Some numerical examples are given.