Abstract
We obtain an exact order estimate for the best approximation of the classes \(L_{\beta ,p}^\Psi \) of functions of one variable in the space L ∞.
Similar content being viewed by others
REFERENCES
A. I. Stepanets, Classification and Approximation of Periodic Functions [in Russian], Naukova Dumka, Kiev (1987).
2. A. S. Fedorenko, “The best m-term trigonometric approximations of functions from the classes \(L_{\beta , p}^\psi\),” in: Fourier Sums: Theory and Applications [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998).
A. S. Fedorenko, “On the best m-term trigonometric and orthogonal trigonometric approximations of functions from the classes \(L_{\beta , p}^\psi\),” Ukr. Mat. Zh., 51, No. 12, 1719–1721 (1999).
A. S. Fedorenko, “The best m-term trigonometric approximations of classes of (Ψ,β)-differentiable functions of one variable,” Ukr. Mat. Zh., 52, No. 6, 850–856 (2000).
E. S. Belinskii, “Decomposition theorems and approximation by a “floating” system of exponentials,” Trans. Amer. Math. Soc., 350, No. 1, 43–53 (1998).
S. M. Nikol'skii, Approximation of Functions of Many Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1989).
A. S. Romanyuk, “Inequalities for the L p-norms of (Ψ,β)-derivatives and the Kolmogorov widths of the classes \(L_{\beta , p}^\psi\), of functions? of many variables,” in: Investigations in the Theory of Approximation of Functions [in Russian], Institute of Mathematics,?Ukrainian Academy of Sciences, Kiev (1987).
A. S. Fedorenko, “On the best m-term trigonometric approximations of classes of (Ψ,β)-differentiable functions of one variable,” in: Boundary-Value Problems for Differential Equations [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fedorenko, A.S., Fedorenko, O.S. The Best m-Term Trigonometric Approximations of the Classes \(L_{\beta ,p}^\Psi \) in Uniform Metric. Ukrainian Mathematical Journal 56, 161–165 (2004). https://doi.org/10.1023/B:UKMA.0000031711.54563.58
Issue Date:
DOI: https://doi.org/10.1023/B:UKMA.0000031711.54563.58