Copositive approximation of periodic functions |
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Authors: | G. A. Dzyubenko J. Gilewicz |
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Affiliation: | (1) International Mathematical Center of NAS of Ukraine, 01601, Tereschenkivs’ka str., 3, Kyiv, Ukraine;(2) Toulon University and Centre de Physique Théorique, CNRS — Luminy, Case 907, 13288 Marseille Cedex 09, France |
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Abstract: | Let f be a real continuous 2π-periodic function changing its sign in the fixed distinct points y i ∈ Y:= {y i } i∈ℤ such that for x ∈ [y i , y i−1], f(x) ≧ 0 if i is odd and f(x) ≦ 0 if i is even. Then for each n ≧ N(Y) we construct a trigonometric polynomial P n of order ≦ n, changing its sign at the same points y i ∈ Y as f, and where N(Y) is a constant depending only on Y, c(s) is a constant depending only on s, ω 3(f, t) is the third modulus of smoothness of f and ∥ · ∥ is the max-norm. This work was done while the first author was visiting CPT-CNRS, Luminy, France, in June 2006. |
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Keywords: | KeywordHeading" > and phrases copositive polynomial approximation uniform estimates |
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