On optimal recovery methods in Hardy-Sobolev spaces (Q2759302)

Let \(W\) be a convex central symmetric set in a linear space \(X\), and \(I:= (\ell_1, \ell_2, \dots, \ell_n)\) be the information operator. Here \(\ell_j \in X^*\), \(1\leq i\leq d\). Let \(S_0\): image \(I\to\mathbb{R}\) (or \(\mathbb{C})\) be a solution of the problem \(\sup_{x\in W} |Lx-S(Ix) |\to \inf\) over the set \(S\): image \(I\to \mathbb{R}\). Then \(S_0\) is called an optimal recovery method for \(L\in X^*\) on the set \(W\). The authors proposed a general approach to find out \(S_0\) basing on a solution to the dual extremal problem. The approach applied to optimal recovery problems in Hardy-Sobolev classes with \(I\) defined by Fourier coefficients and evaluations.