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\title{Optimal recovery and best quadratures for Hardy--Sobolev classes}
\author{Konstantin Yu. Osipenko}

\maketitle

Denote by $H_\infty^r$ the class of analytic in the unit disk $D$ functions
$f$ for which $|f^{(r)}(z)|\le1$, $z\in D$. Using a general approach for
the construction of optimal recovery methods of linear functionals, we
obtain optimal recovery methods and best quadrature formulas for
Hardy--Sobolev classes $H_\infty^r$. We find a linear space of analytic
functions which play the same role as polynomials splines in the similar
problem for Sobolev classes.

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