Geodesic
Best approximation of differentiation operators on the Sobolev class of functions analytic in a strip
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1286-1298

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A solution is obtained for interconnected extremal problems on the class of analytic functions in a strip with finite $L^2$-norms of limit values of functions on one boundary line and bounded $L^2$-norms of limit values of the derivative of order $n, n\ge 0,$ on the other boundary line: best approximation of the differentiation operators with respect to the uniform norm on an intermediate line by bounded operators; optimal recovery of the derivative of order k on an intermediate line from values of the function on the boundary line given with an error. An exact Kolmogorov-type inequality is obtained that estimates the uniform norm of the derivative of order $k$ on an intermediate line in terms of the $L^2$-norm of the limit boundary values of the function and the derivative of order $n.$
Keywords: analytic functions, best approximation of the operator, optimal recovery, Kolmogorov inequality. 
@article{SEMR_2021_18_2_a70,
     author = {R. R. Akopyan},
     title = {Best approximation of differentiation operators on the {Sobolev} class of functions analytic in a strip},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1286--1298},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a70/}
}
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R. R. Akopyan. Best approximation of differentiation operators on the Sobolev class of functions analytic in a strip. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1286-1298. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a70/