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Approximation of periodic functions by Fejer-Zygmund means in various metrics

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Literature cited

  1. A. Zygmund, “The approximation of functions by typical means of their Fourier series,” Duke Math. J.,12, No. 4, 695–704 (1945).

    Google Scholar 

  2. A. F. Timan, Theory of Approximation of Functions of a Real Variable [in Russian], Fizmatgiz, Moscow (1960).

    Google Scholar 

  3. N. A. Il'yasov, “Approximation of periodic functions by Zygmund means,” Mat. Zametki,39, No. 3, 367–382 (1986).

    Google Scholar 

  4. N. A. Il'yasov, “Imbedding theorems for some classes of periodic functions in Lp, 1≤ p ≤ ∞,” Dokl. Akad. Nauk SSSR,276, No. 6, 1301–1304 (1984).

    Google Scholar 

  5. N. T. Temirgaliev, “Imbedding some classes of functions,” Mat. Zametki,20, No. 6, 835–841 (1976).

    Google Scholar 

  6. V. I. Kolyada, “Imbedding theorems and inequalities for various metrics for best approximations,” Mat. Sb.,102, No. 2, 195–215 (1977).

    Google Scholar 

  7. M. F. Timan, “Imbedding classes of functions in L (k)p ,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 61–74 (1974).

    Google Scholar 

  8. M. F. Timan, “Orthonormal systems satisfying an inequality of S. M. Nikol'skii,” Anal. Math.,4, No. 1, 75–82 (1978).

    Google Scholar 

  9. P. L. Ul'yanov, “Imbedding theorems and relations between best approximations (by moduli of continuity) in various metrics,” Mat. Sb.,81, No. 1, 104–131 (1970).

    Google Scholar 

  10. O. V. Besov, “Conditions for derivatives of periodic functions to belong to Lp,” Nauch. Dokl. Vyssh. Shk. Fiz.-Mat. N., No. 1, 13–17 (1959).

    Google Scholar 

  11. M. F. Timan, “Inverse theorems of the constructive theory of functions in the spaces Lp (1 ≤ p ≤ ∞),” Mat. Sb.,46, No. 1, 125–132 (1958).

    Google Scholar 

  12. G. Hardy, J. Littlewood, and G. Polya, Inequalities [Russian translation], IL, Moscow (1948).

    Google Scholar 

  13. V. E. Geit, “Sharpness of some inequalities in the theory of approximation,” Mat. Zametki,10, No. 5, 571–582 (1971).

    Google Scholar 

  14. A. Zygmund, Trigonometric Series [Russian translation], Vols. 1, 2, Mir, Moscow (1965).

    Google Scholar 

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Authors and Affiliations

  1. S. M. Kirov Azerbaidzhan State University, USSR

    N. A. Il'yasov

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  1. N. A. Il'yasov
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Translated from Matematicheskie Zametki, Vol. 48, No. 4, pp. 48–57, October, 1990.

The author thanks S. B. Stechkin for posing the problem and interest in the work.

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Il'yasov, N.A. Approximation of periodic functions by Fejer-Zygmund means in various metrics. Mathematical Notes of the Academy of Sciences of the USSR 48, 1004–1010 (1990). https://doi.org/10.1007/BF01139600

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