Geodesic
On the best approximation of the differentiation operator on the half-line
Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 573-582

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We solve a problem of S. B. Stechkin concerning the best approximation in the metric of $C$ to the operator of $k$-th order differentiation on certain classes of differentiable functions defined on the half-line, by linear operators whose norms from $L_2$ into $C$ are bounded. We consider the analogous problem for linear differential operators with constant coefficients. 
@article{MZM_1969_6_5_a7,
     author = {V. N. Gabushin},
     title = {On the best approximation of the differentiation operator on the half-line},
     journal = {Matemati\v{c}eskie zametki},
     pages = {573--582},
     publisher = {mathdoc},
     volume = {6},
     number = {5},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a7/}
}
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V. N. Gabushin. On the best approximation of the differentiation operator on the half-line. Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 573-582. http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a7/