Geodesic
Kolmogorov-type inequalities and the best formulas for numerical differentiation
Matematičeskie zametki, Tome 4 (1968) no. 2, pp. 233-238.

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For a certain class of complex-valued functions $f(x)$, $-\infty$, is found the best approximation $$ u_N=\inf_{\|A\|\le N}\sup_{\|f^{(n)}\|_{L_2}\le1}\|f^{(k)}-A(f)\|C $$ of a differential operator by linear operators $A$ with the norm $\|A\|_{L_2}^C\le N$, $N>0$. Using the value $u_N$, the smallest constant $Q$ in the inequality $$ \|f^{(k)}\|_Q\le Q\|f\|_{L_2}^\alpha\|f^{(n)}\|^\beta_{L_2} $$ is found. 
@article{MZM_1968_4_2_a14,
     author = {L. V. Taikov},
     title = {Kolmogorov-type inequalities and the best formulas for numerical differentiation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {233--238},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_2_a14/}
}
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L. V. Taikov. Kolmogorov-type inequalities and the best formulas for numerical differentiation. Matematičeskie zametki, Tome 4 (1968) no. 2, pp. 233-238. http://geodesic.mathdoc.fr/item/MZM_1968_4_2_a14/