MEAN DIMENSION, WIDTHS, AND OPTIMAL RECOVERY OF SOBOLEV CLASSES OF FUNCTIONS ON THE LINE

Authors
MAGARILILYAEV GG
Citation
Gg. Magarililyaev, MEAN DIMENSION, WIDTHS, AND OPTIMAL RECOVERY OF SOBOLEV CLASSES OF FUNCTIONS ON THE LINE, Mathematics of the USSR. Sbornik, 74(2), 1993, pp. 381-403
Citations number
30
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Mathematics of the USSR. Sbornik → ACNP
ISSN journal
00255734
Volume
74
Issue
2
Year of publication
1993
Pages
381 - 403
Database
ISI
SICI code
0025-5734(1993)74:2<381:MDWAOR>2.0.ZU;2-H
Abstract
The concept of mean dimension is introduced for a broad class of subsp aces of L(p)(R) , and analogues of the Kolmogorov widths, Bernstein wi dths, Gel'fand widths, and linear widths are defined. The precise valu es of these quantities are computed for Sobolev classes of functions o n R in compatible metrics, and the corresponding extremal spaces and o perators are described. A closely related problem of optimal recovery of functions in Sobolev classes is also studied.