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- Title
Exact constants in Jackson inequalities for periodic differentiable functions in the space L.
- Authors
Pichugov, S.
- Abstract
It is proved that, in the space L[0, 2π], the following equalities hold for all k = 0, 1, 2, ..., n ∈ ℕ, r = 1, 3, 5, ..., µ≥ r: [Figure not available: see fulltext.] where E( f) and E( f) are the best approximations of f by, respectively, trigonometric polynomials of degree n − 1 and 2 π-periodic splines of minimal deficiency of order µ with 2 n equidistant nodes, ω( f, h) is the modulus of continuity of f, Ψ is the rth periodic integral of the special function Ψ, which is odd and piecewise constant on the partition jπ/(2 k + 1), j ∈ ℤ. For k = 0, this result was obtained earlier by Ligun.
- Subjects
TRIGONOMETRY; SPHERICAL trigonometry; FOURIER analysis; PIECEWISE affine systems; PIECEWISE linear topology
- Publication
Mathematical Notes, 2014, Vol 96, Issue 1/2, p261
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S000143461407027X