Geodesic
Best and optimal recovery methods for classes of harmonic functions
Sbornik. Mathematics, Tome 73 (1992) no. 1, pp. 111-133

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The author considers problems of best recovery of a functional $L_u=\lambda_0u(x)+\dots+\lambda_ku^{(k)}(x)$, $x\in(-1,1)$, in the space $h_p$ of harmonic functions for $p=\infty$ or 2, in terms of the values of the functions and their derivatives at points of the interval $(-1,1)$. In the space $h_\infty$ the problem of constructing best quadrature formulas is solved. The existence of optimal quadrature formulas is proved, and, under certain conditions, the uniqueness of the optimal knots. 
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     author = {K. Yu. Osipenko},
     title = {Best and optimal recovery methods for classes of harmonic functions},
     journal = {Sbornik. Mathematics},
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     number = {1},
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K. Yu. Osipenko. Best and optimal recovery methods for classes of harmonic functions. Sbornik. Mathematics, Tome 73 (1992) no. 1, pp. 111-133. http://geodesic.mathdoc.fr/item/SM_1992_73_1_a6/