Geodesic
Mean dimension, widths, and optimal recovery of Sobolev classes of functions on the line
Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 381-403

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

The concept of mean dimension is introduced for a broad class of subspaces of $L_p(\mathbf R)$, and analogues of the Kolmogorov widths, Bernstein widths, Gel'fand widths, and linear widths are defined. The precise values of these quantities are computed for Sobolev classes of functions on $\mathbf R$ in compatible metrics, and the corresponding extremal spaces and operators are described. A closely related problem of optimal recovery of functions in Sobolev classes is also studied. 
@article{SM_1993_74_2_a5,
     author = {G. G. Magaril-Il'yaev},
     title = {Mean dimension, widths, and optimal recovery of {Sobolev} classes of functions on the line},
     journal = {Sbornik. Mathematics},
     pages = {381--403},
     publisher = {mathdoc},
     volume = {74},
     number = {2},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_74_2_a5/}
}
TY  - JOUR
AU  - G. G. Magaril-Il'yaev
TI  - Mean dimension, widths, and optimal recovery of Sobolev classes of functions on the line
JO  - Sbornik. Mathematics
PY  - 1993
SP  - 381
EP  - 403
VL  - 74
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1993_74_2_a5/
LA  - en
ID  - SM_1993_74_2_a5
ER  - 
%0 Journal Article
%A G. G. Magaril-Il'yaev
%T Mean dimension, widths, and optimal recovery of Sobolev classes of functions on the line
%J Sbornik. Mathematics
%D 1993
%P 381-403
%V 74
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1993_74_2_a5/
%G en
%F SM_1993_74_2_a5
G. G. Magaril-Il'yaev. Mean dimension, widths, and optimal recovery of Sobolev classes of functions on the line. Sbornik. Mathematics, Tome 74 (1993) no. 2, pp. 381-403. http://geodesic.mathdoc.fr/item/SM_1993_74_2_a5/