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- Title
Exact values of best approximations for classes of periodic functions by splines of deficiency 2.
- Authors
Babenko, V.; Parfinovich, N.
- Abstract
We obtain exact values of best L1-approximations for the classes W r F, r ∈ ℕ, of periodic functions whose rth derivative belongs to a given rearrangement-invariant set F as well as for the classes W r H ω of periodic functions whose rth derivative has a given convex (up) majorant ω( t) of the modulus of continuity by subspaces of polynomial splines of order m ≥ r + 1 of deficiency 2 with nodes at the points 2 kπ/n, n ∈ ℕ, k ∈ ℤ. It is shown that these subspaces are extremal for the Kolmogorov widths of the corresponding function classes.
- Subjects
PERIODIC functions; KOLMOGOROV complexity; INVARIANT sets; CONTINUITY; APPROXIMATION theory
- Publication
Mathematical Notes, 2009, Vol 85, Issue 3/4, p515
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434609030237