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Trigonometric approximation with exponential error orders

I. construction of asymptotically optimal processes; generalized de la Vallée Poussin sums

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References

  1. Achieser, N. I.: Vorlesungen über Approximationstheorie. Berlin: Akademie Verlag 1967

    Google Scholar 

  2. Berens, H.: Interpolationsmethoden zur Behandlung von Approximationsprozessen auf Banachräumen. Lecture Notes in Mathematics 64. Berlin, Heidelberg, New York: Springer 1967

    Google Scholar 

  3. Butzer, P. L., Nessel, R. J.: Fourier analysis and approximation. Vol. I. Basel: Birkhäuser 1971

    Google Scholar 

  4. Dahmen, W.: Trigonometric approximation with exponential error orders II: Properties of asymptotically optimal processes; impossibility of arbitrarily good error estimates. (to appear)

  5. Dahmen, W.: Trigonometric approximation with exponential error orders III: Criteria for asymptotically optimal processes. (to appear)

  6. Dahmen, W., Görlich, E.: A conjecture of Golomb on optimal and nearly-optimal approximation. Bull. Amer. Math. Soc.80, 1199–1202 (1974)

    Google Scholar 

  7. Dahmen, W., Görlich, E.: Asymptotically optimal linear approximation processes and a conjecture of Golomb. In: Linear Operators and Approximation II (ed. by P. L. Butzer and B. Sz.-Nagy) ISNM Vol. 25. Basel: Birkhäuser 1974

    Google Scholar 

  8. Dahmen, W., Görlich, E.: Best approximation with exponential orders and intermediate spaces. Math. Z.148, 7–21 (1976)

    Google Scholar 

  9. Dahmen, W., Görlich, E.: The characterization problem for best approximation with exponential error orders and evaluation of entropy. Math. Nachr. 1976 (in print)

  10. du Bois-Reymond, P.: Sur la grandeur relative des infinis des fonctions. Annali di Mat. Pura e Appl.4, 338–353 (1971)

    Google Scholar 

  11. Görlich, E.: Logarithmic and exponential variants of Bernstein's inequality and generalized derivatives. In: Linear operators and approximation (ed. by P. L. Butzer, J.-P. Kahane and B. Sz.-Nagy), ISNM 20. Basel: Birkhäuser 1972

    Google Scholar 

  12. Golomb, M.: Optimal and nearly-optimal linear approximation. In: Approximation of functions (ed. by H. L. Garabedian), Amsterdam: Elsevier 1965

    Google Scholar 

  13. Golomb, M.: Lectures on theory of approximation. Mimeographed Lecture Notes. Argonne National Laboratory 1962

  14. Korneičuk, N. P.: On methods of investigating extremal problems in the theory of best approximation. Russian Math. Surveys29, 7–43 (1974)

    Google Scholar 

  15. Leindler, L.: On summability of Fourier series. Acta. Sci. Math. (Szeged)29, 147–162 (1968)

    Google Scholar 

  16. Lorentz, G. G.: Metric entropy, widths and superpositions of functions. Amer. Math. mthly.69, 469–485 (1962)

    Google Scholar 

  17. Lorentz, G. G.: Metric entropy and approximation. Bull. Amer. Math. Soc.72, 903–937 (1966)

    Google Scholar 

  18. Stečkin, S. B.: On de la Vallée Poussin sums. Dokl. Akad. Nauk SSSR (NS)80, 545–548 (1951)

    Google Scholar 

  19. Teljakovskiñ, S. A.: Approximation of differentiable functions by de la Vallée Poussin's sums. Dokl. Akad. Nauk SSSR121, 426–429 (1958)

    Google Scholar 

  20. Timan, A. F.: Theory of approximation of functions of a real variable. Oxford: Pergamon Press 1963

    Google Scholar 

  21. Zygmund, A.: Trigonometric series I. Cambridge: Cambridge University Press 1959

    Google Scholar 

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Dahmen, W. Trigonometric approximation with exponential error orders. Math. Ann. 230, 57–74 (1977). https://doi.org/10.1007/BF01420576

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