Geodesic
On the best mean square approximations by entire functions of exponential type in $L_2(\mathbb R)$ and mean $\nu$-widths of some functional classes
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2014), pp. 30-48

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

We consider some extremal problems of approximation theory of functions at the whole real axis $\mathbb R$ by entire functions of the exponential type. In particular, we find the exact values of the mean $\nu$-widths of classes of functions, defined by the moduli of continuity of $m$th order $\omega_m$ and majorants $\Psi$ satisfying the special type of restriction.
Keywords: best approximation, entire function of exponential type, modulus of continuity, mean $\nu$-width
Mots-clés : majorant. 
@article{IVM_2014_7_a2,
     author = {S. B. Vakarchuk and M. Sh. Shabozov and M. R. Langarshoev},
     title = {On the best mean square approximations by entire functions of exponential type in $L_2(\mathbb R)$ and mean $\nu$-widths of some functional classes},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {30--48},
     publisher = {mathdoc},
     number = {7},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_7_a2/}
}
TY  - JOUR
AU  - S. B. Vakarchuk
AU  - M. Sh. Shabozov
AU  - M. R. Langarshoev
TI  - On the best mean square approximations by entire functions of exponential type in $L_2(\mathbb R)$ and mean $\nu$-widths of some functional classes
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2014
SP  - 30
EP  - 48
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2014_7_a2/
LA  - ru
ID  - IVM_2014_7_a2
ER  - 
%0 Journal Article
%A S. B. Vakarchuk
%A M. Sh. Shabozov
%A M. R. Langarshoev
%T On the best mean square approximations by entire functions of exponential type in $L_2(\mathbb R)$ and mean $\nu$-widths of some functional classes
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2014
%P 30-48
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2014_7_a2/
%G ru
%F IVM_2014_7_a2
S. B. Vakarchuk; M. Sh. Shabozov; M. R. Langarshoev. On the best mean square approximations by entire functions of exponential type in $L_2(\mathbb R)$ and mean $\nu$-widths of some functional classes. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2014), pp. 30-48. http://geodesic.mathdoc.fr/item/IVM_2014_7_a2/