Geodesic
The Carath\'eodory--Fej\'er problem and optimal recovery of derivatives in Hardy spaces
Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 21-33

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The Carathéodory–Fejér problem in the Hardy spaces $ H_p$ is reduced to solving systems of a certain form. The optimal method of recovery of the derivative of any order of a function in $H_p$ from its values on a collection of points is expressed in terms of the solution of a system of the same type. The analogous problem of recovery is considered in the space $h_\infty$ of bounded harmonic functions. 
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     author = {K. Yu. Osipenko},
     title = {The {Carath\'eodory--Fej\'er} problem and optimal recovery of derivatives in {Hardy} spaces},
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K. Yu. Osipenko. The Carath\'eodory--Fej\'er problem and optimal recovery of derivatives in Hardy spaces. Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 21-33. http://geodesic.mathdoc.fr/item/SM_1995_81_1_a1/