Research output: Contribution to journal › Article › peer-review
Let σ > 0, m, r ∈ ℕ, m ≥ r, let Sσ,m be the space of splines of order m and minimal defect with nodes jπσ (j ∈ ℤ), and let Aσ,m(f)p be the best approximation of a function f by the set Sσ,m in the space Lp(ℝ). It is known that for p = 1,+∞, (Formula presented.) where Kr are the Favard constants. In this paper, linear operators Xσ,r,m with values in Sσ,m such that for all p ∈ [1,+∞] and f ∈ Wp (r)(ℝ),ǁf−Xσ,r,m(f)ǁp≤Kr/σrǁf(r)ǁp are constructed. This proves that the upper bounds indicated above can be achieved by linear methods of approximation, which was previously unknown. Bibliography: 21 titles.
Original language | English |
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Pages (from-to) | 3-22 |
Number of pages | 20 |
Journal | Journal of Mathematical Sciences (United States) |
Volume | 217 |
Issue number | 1 |
Early online date | 7 Jul 2016 |
DOIs | |
State | Published - 1 Aug 2016 |
ID: 15680306