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Best approximations by rational vector functions in Hardy spaces. (Russian) Zbl 0629.30034
Two problems of the best approximation in the vector-valued Hardy space \(H^ 2(E)\) in the unit disk are considered, the best approximation by rational functions with prescribed singularities and the best approximation by rational functions of a fixed degree. The author proves that in both cases the function of the best approximation exists and gives the solution of the corresponding interpolation problems.
Reviewer: J.Ljubarski

MSC:
30D55 \(H^p\)-classes (MSC2000)
30E10 Approximation in the complex plane
41A20 Approximation by rational functions
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