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- W2007024144 abstract "We investigate the branching of solutions of a Hammerstein-type nonlinear two-dimensional integral equation that arises in the problems of mean-square approximation of a real finite nonnegative function of two variables by the modulus of double Fourier integral, depending on two parameters [Mat. Metody Fiz.-Mekh. Polya, 51, No. 1, 53–64; No. 4, 80–85 (2008)]. We have derived analytical expressions for eigenfunctions of the corresponding linear homogeneous integral equation, necessary for the construction of branched-off solutions, and obtained systems of transcendental equations for finding the points of their branching. We also present, in the first approximation, the analytical representations of complex solutions branched-off from the real solution for the two-dimensional case of branching." @default.
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- W2007024144 date "2011-12-28" @default.
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- W2007024144 title "Branching of solutions for the problem of mean-square approximation of a real finite function of two variables by the modulus of double Fourier transformation" @default.
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- W2007024144 doi "https://doi.org/10.1007/s10958-011-0628-8" @default.
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