One-sided widths of classes of smooth functions
Ural mathematical journal, Tome 1 (2015) no. 1, pp. 83-86
Cet article a éte moissonné depuis la source Math-Net.Ru
One-sided widths of the classes of functions $W_p^r[0,1]$ in the metric $L_q[0,1],$ $1\le p,q \le \infty,\ r>1$, are studied. Such widths are defined similarly to Kolmogorov widths with additional constraints on the approximating functions.
Keywords:
One-sided widths, Exact orders, Classes of smooth functions.
@article{UMJ_2015_1_1_a7,
author = {Yurii N. Subbotin},
title = {One-sided widths of classes of smooth functions},
journal = {Ural mathematical journal},
pages = {83--86},
year = {2015},
volume = {1},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/UMJ_2015_1_1_a7/}
}
Yurii N. Subbotin. One-sided widths of classes of smooth functions. Ural mathematical journal, Tome 1 (2015) no. 1, pp. 83-86. http://geodesic.mathdoc.fr/item/UMJ_2015_1_1_a7/
[1] Kolmogoroff A., “Uber die beste Annaherung von Funktionen einer geqebenen Functionenklasse”, Ann. Math, 37 (1936), 107–111
[2] Korneichuk N.P., Ligun A.A. and Doronin V.G., Approximation With Constraints, Naukova Dumka, Kiev, 1982, 250 pp. (in Russian)
[3] Kashin B.S., “Diameters of some finite-dimensional sets and classes of smooth functions”, Izv. Math, 11:2 (1977), 334–351
[4] Birkhoff G., Schultz M.H. and Varga R.S., “Piecewise Hermite interpolation in one and two variables with application to partial differential equations”, Numer. Math, 11 (1968), 232–256