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Orders of the orthoprojection widths of classes of periodic functions of one and of several variables. (English. Russian original) Zbl 0712.42023
Math. Notes 43, No. 2, 110-118 (1988); translation from Mat. Zametki 43, No. 2, 197-211 (1988).
See the review in Zbl 0659.42008.

MSC:
42A75 Classical almost periodic functions, mean periodic functions
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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[1] ?. M. Galeev, ?Approximation of classes of functions with several bounded derivatives by Fourier sums,? Mat. Zametki,23, No. 2, 197-211 (1978). · Zbl 0467.42003
[2] V. N. Temlyakov, ?Widths of certain classes of functions of several variables,? Dokl. Akad. Nauk SSSR,267, No. 2, 314-317 (1982).
[3] V. M. Tikhomirov, Certain Questions of Approximation Theory [in Russian], Moscow State Univ. (1976). · Zbl 0346.41004
[4] 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).
[5] R. S. Ismagilov, ?Widths of sets in normed linear spaces and approximation of functions by trigonometric polynomials,? Usp. Mat. Nauk,29, No. 3, 161-178 (1974). · Zbl 0303.41039
[6] B. S. Kashin, ?Widths of certain finite-dimensional sets and classes of smooth functions,? Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 2, 334-351 (1977).
[7] ?. M. Galeev, ?The Kolmogorov widths of certain classes of periodic functions of several variables,? in: Constructive Theory of Functions [in Russian], Proceedings of the International Conference on Constructive Theory of Functions, Sofia (1984), pp. 27-32.
[8] ?. M. Galeev, ?The Kolmogorov widths of classes of periodic functions with several bounded derivatives,? in: Collection of Works of the Conference of Young Scientists of Moscow State University [in Russian], 1984.
[9] ?. M. Galeev, ?The Kolmogorov widths of classes \(\tilde W_P^{\bar \alpha }\) and \(\tilde H_P^{\bar \alpha }\) of periodic functions of several variables in the space \(\tilde L_q\) ,? Izv. Akad. Nauk SSSR, Ser. Mat.,49, No. 5, 916-934 (1985). · Zbl 0626.41018
[10] 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). · Zbl 0499.42002
[11] O. V. Besov, V. P. Il’in, and S. M. Nikol’skii, Integral Representations of Functions and Embedding Theorems [in Russian], Nauka, Moscow (1975).
[12] A. Zygmund, Trigonometric Series, Vol. 2, Cambridge Univ. Press (1959). · Zbl 0085.05601
[13] ?. M. Galeev, ?Approximation of classes of periodic functions with several bounded derivatives,? Candidate’s Dissertation, Physicomathematical Sciences, Moscow (1978). · Zbl 0467.42003
[14] E. D. Gluskin, ?On certain finite-dimensional problems of theory of widths,? Vestn. Leningr. Gos. Univ., Mat., No. 13, 5-10 (1981). · Zbl 0482.41018
[15] Din’ Zung, ?On the approximation of periodic functions of several variables,? Usp. Mat. Nauk,38, No. 6, 111-112 (1983). · Zbl 0541.42010
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