Abstract
We investigate problems related to the approximation by linear methods and the best approximations of the classes \(B_{p,{\theta }}^r\), 1 ≤ p ≤ ∞ in the space L ∞.
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REFERENCES
S. M. Nikol'skii, Approximation of Functions of Many Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1969).
V. N. Temlyakov, “Approximation of functions with bounded mixed derivative,” Tr. Mat. Inst. Akad. Nauk SSSR, 178, 1–112 (1986).
W. Dahmen and E. Gorlich, “A conjecture of M. Golomb on optimal and nearly-optimal approximation,” Bull. Amer. Math. Soc., 80, No. 6, 1199–1202 (1974).
V. N. Temlyakov, “Approximation of functions with bounded mixed difference by trigonometric polynomials and widths of certain classes of functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 46, No. 1, 171–186 (1982).
V. N. Temlyakov, “Approximation of periodic functions of several variables by trigonometric polynomials and widths of certain classes of functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 49, No. 5, 986–1030 (1985).
S. M. Nikol'skii, “Inequalities for entire functions of finite order and their application to the theory of differentiable functions of many variables,” Tr. Mat. Inst. Akad. Nauk SSSR, 38, 244–278 (1951).
D. Jackson, “Certain problem of closest approximation,” Bull. Amer. Math. Soc., 39, No. 12, 889–906 (1933).
J. Marcinkiewicz, “Quelques remarques sur l'interpolation,” Acta Litt. Acad. Sci. Szeged, 8, 127–130 (1937).
A. S. Romanyuk, “On estimates for approximation characteristics of the Besov classes of periodic functions of many variables,” Ukr. Mat. Zh., 49, No. 9, 1250–1261 (1997).
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Romanyuk, A.S. Approximation of Classes B r p,θ by Linear Methods and Best Approximations. Ukrainian Mathematical Journal 54, 825–838 (2002). https://doi.org/10.1023/A:1021691615557
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DOI: https://doi.org/10.1023/A:1021691615557