Abstract
Abstract The interpolation problem of reconstruction of a holomorphic in the upper half-plane function with non-negative imaginary part and continuous boundary value on the real axis by the first 2n + 1 terms of its asymptotic decomposition at infinity and its values at some m points of the real axis is solved using algorithms, which are reminiscent of those of Schur and Lagrange. At the same time some algorithms are obtained for reconstruction of holomorphic in the upper half-plane contractive functions with continuous boundary values by their values at some m real points. The corresponding interpolation problems are generalized to include values of the first derivative of the sought functions at some real points.
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