Geodesic
Optimal rate of integration and $\varepsilon$-entropy of a~class of analytic functions
Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 3-10.

Voir la notice de l'article provenant de la source Math-Net.Ru

The author considers a class $F$ of analytic functions real in the interval $[-1,1]$ and bounded in the unit circle. As an estimate of the optimal quadrature error $R(n)$ over the class $F$ it is shown that $$ e^{\left(-2\sqrt2+\frac1{\sqrt2}\right)\pi\sqrt n}\le R(n)\le e{-\frac\pi{\sqrt2}n}. $$ With the additional condition that $\max\limits_{x\in[-1,1]}|f(x)|\le B$, an estimate is obtained for the $\varepsilon$-entropy $H_\varepsilon(F)$: $$ \frac8{27}\frac{(\ln2)^2}{\pi^2}\le\lim\frac{H_\varepsilon(F)}{(\log\frac1\varepsilon)^3}\le\frac2{\pi^2}(\ln2)^2. $$ 
@article{MZM_1973_14_1_a0,
     author = {B. D. Boyanov},
     title = {Optimal rate of integration and $\varepsilon$-entropy of a~class of analytic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {3--10},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a0/}
}
TY  - JOUR
AU  - B. D. Boyanov
TI  - Optimal rate of integration and $\varepsilon$-entropy of a~class of analytic functions
JO  - Matematičeskie zametki
PY  - 1973
SP  - 3
EP  - 10
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a0/
LA  - ru
ID  - MZM_1973_14_1_a0
ER  - 
%0 Journal Article
%A B. D. Boyanov
%T Optimal rate of integration and $\varepsilon$-entropy of a~class of analytic functions
%J Matematičeskie zametki
%D 1973
%P 3-10
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a0/
%G ru
%F MZM_1973_14_1_a0
B. D. Boyanov. Optimal rate of integration and $\varepsilon$-entropy of a~class of analytic functions. Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 3-10. http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a0/