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Optimal recovery of differentiable functions. (English. Russian original) Zbl 0728.41033
Math. USSR, Sb. 69, No. 2, 357-377 (1991); translation from Mat. Sb. 181, No. 3, 334-353 (1990).
Optimal restoration of differentiable functions is investigated for $$W^ L_{\infty,\sigma}(I)=\{f\in L^ r_{\infty}(I):| Lf(x)| \leq \sigma (x),\quad \forall x\in I\},$$ where L is a given differential operator of r-order, and $$\sigma$$ ($$\cdot): I\to {\mathbb{R}}$$ a given continuous function.

##### MSC:
 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
##### Keywords:
Optimal restoration
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