Abstract
We obtain order estimates for linear widths of the Besov classes \(B_{p,\theta}^r\) of periodic functions of many variables in the space L q for certain values of the parameters p and q.
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REFERENCES
A. S. Romanyuk, “On Kolmogorov widths of classes B r p , pΘ of periodic functions of many variables with low smoothness in the space L q,” Ukr. Mat. Zh. 46, No. 7, 915-926 (1994).
A. S. Romanyuk, “On the best approximations and Kolmogorov widths of Besov classes of periodic functions of many variables,” Ukr. Mat. Zh. 47, No. 1, 79-92 (1995).
A. S. Romanyuk, “Trigonometric widths of the classes B r p , pΘ of functions of many variables in the space L q,” Ukr. Mat. Zh. 50, No. 8, 1089-1097 (1998).
S. M. Nikol'skii, Approximation of Functions of Many Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1969).
V. M. Tikhomirov, “Widths of sets in a functional space and the theory of the best approximations,” Usp. Mat. Nauk 15, No. 3, 81-120 (1960).
A. Kolmogoroff, “Ñber die beste Annaherung von Funktionen einer gegeben Funktionenklasse,” Ann. Math. 37, 107-111 (1936).
E. D. Gluskin, “Norms of random matrices and widths of finite-dimensional sets,” Mat. Sb. 120, No. 2, 180-189 (1983).
B. S. Kashin, “On some properties of the matrices of bounded operators from the space l n 2 to l m 2 ,” Izv. Akad. Nauk Arm. SSR, Ser. Mat. 15, No. 5, 379-394 (1980).
É. M. Galeev, “Kolmogorov widths of classes of periodic functions of many variables \({\tilde W}\) r p and \({\tilde H}\) r p in the space \({\tilde L}\) q,” Izv. Akad. Nauk SSSR, Ser. Mat. 49, No. 5, 916-934 (1985).
A. Zygmund, Trigonometric Series [Russian translation], Vols. 1, 2, Mir, Moscow (1965).
É. M. Galeev, “Linear widths of Hölder-Nikol'skii classes of periodic functions of many variables,” Mat. Zametki 59, No. 2, 189-199 (1996).
V. N. Temlyakov, “Approximation of functions with bounded mixed derivative,” Tr. Mat. Inst. Akad. Nauk SSSR 178, 1-112 (1986).
É. S. Belinskii and É. M. Galeev, “On the minimum value of the norms of mixed derivatives of trigonometric polynomials with given number of harmonics,” Vestn. Mosk. Univ., Mat. Mekh. No. 2, 3–7 (1991).
A. S. Romanyuk, “Approximation of Besov classes of periodic functions of many variables in the space L q,” Ukr. Mat. Zh. 43, No. 10, 1398-1408 (1991).
A. S. Romanyuk, “Best trigonometric and bilinear approximations for Besov classes of functions of many variables,” Ukr. Mat. Zh. 47, No. 8, 1097-1111 (1995).
A. S. Romanyuk, “Best trigonometric approximations and Kolmogorov widths of Besov classes of functions of many variables,” Ukr. Mat. Zh. 45, No. 5, 663-675 (1993).
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Romanyuk, A.S. Linear Widths of the Besov Classes of Periodic Functions of Many Variables. I. Ukrainian Mathematical Journal 53, 744–761 (2001). https://doi.org/10.1023/A:1012530317130
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DOI: https://doi.org/10.1023/A:1012530317130