Geodesic
Approximation of the differentiation operator on the class of functions analytic in an annulus
Ural mathematical journal, Tome 3 (2017) no. 2, pp. 6-13 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the class of functions analytic in the annulus $C_r:=\left\{z\in\mathbb{C}\, :\, r|z|1\right\}$ with bounded $L^p$-norms on the unit circle, we study the problem of the best approximation of the operator taking the nontangential limit boundary values of a function on the circle $\Gamma_r$ of radius $r$ to values of the derivative of the function on the circle $\Gamma_\rho$ of radius $\rho,\, r\rho1,$ by bounded linear operators from $L^p(\Gamma_r)$ to $L^p(\Gamma_ \rho)$ with norms not exceeding a number $N$. A solution of the problem has been obtained in the case when $N$ belongs to the union of a sequence of intervals. The related problem of optimal recovery of the derivative of a function from boundary values of the function on $\Gamma_\rho$ given with an error has been solved.
Keywords: Best approximation of operators, Optimal recovery, Analytic functions. 
@article{UMJ_2017_3_2_a1,
     author = {Roman R. Akopyan},
     title = {Approximation of the differentiation operator on the class of functions analytic in an annulus},
     journal = {Ural mathematical journal},
     pages = {6--13},
     year = {2017},
     volume = {3},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a1/}
}
TY  - JOUR
AU  - Roman R. Akopyan
TI  - Approximation of the differentiation operator on the class of functions analytic in an annulus
JO  - Ural mathematical journal
PY  - 2017
SP  - 6
EP  - 13
VL  - 3
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a1/
LA  - en
ID  - UMJ_2017_3_2_a1
ER  - 
%0 Journal Article
%A Roman R. Akopyan
%T Approximation of the differentiation operator on the class of functions analytic in an annulus
%J Ural mathematical journal
%D 2017
%P 6-13
%V 3
%N 2
%U http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a1/
%G en
%F UMJ_2017_3_2_a1
Roman R. Akopyan. Approximation of the differentiation operator on the class of functions analytic in an annulus. Ural mathematical journal, Tome 3 (2017) no. 2, pp. 6-13. http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a1/

[1] Akopyan R. R., “Best approximation for the analytic continuation operator on the class of analytic functions in a ring”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:4 (2012), 3–13 (in Russian)

[2] Akopyan R. R., “Best approximation of the differentiation operator on the class of functions analytic in a strip”, Proc. Steklov Inst. Math., 288:Suppl. 1. (2015), S5–S12 | DOI

[3] Arestov V. V., “Approximation of unbounded operators by bounded operators and related extremal problems”, Russ. Math. Surv., 51:6 (1996.), 1093–1126 | DOI

[4] Stechkin S. B., “Inequalities between the norms of derivatives of an arbitrary function”, Acta Sci. Math., 26:3–4 (1965), 225–230

[5] Stechkin S. B., “Best approximation of linear operators”, Math. Notes, 1:2 (1967), 91–99 | DOI

[6] Osipenko K. Yu., Optimal Recovery of Analytic Functions, Nova Science, Huntington, NY, 2000