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On the singular integral of de la Vallée-Poussin

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References

  1. N. I.Achiezer, Vorlesungen Über Approximationstheorie. Berlin 1953.

  2. P. L. Butzer, Dominated convergence of Kantorovitch polynomials in the spaceL p . Trans. roy. Soc. Canada, Ser. III, Sect. III,46, 23–27 (1952).

    Google Scholar 

  3. P. L. Butzer, Linear combinations of Bernstein polynomials. Canadian J. Math.5, 559–567 (1953).

    Google Scholar 

  4. P. L. Butzer andW. Kozakiewicz, On the Riemann derivatives for integrable functions. Canadian J. Math.6, 572–581 (1954).

    Google Scholar 

  5. G. H. Hardy andJ. E. Littlewood, Some properties of fractional integrals. Math. Z.27, 565–606 (1928).

    Google Scholar 

  6. G. H. Hardy andJ. E. Littlewood, A convergence criterion for Fourier series. Math. Z.28, 612–634 (1928).

    Google Scholar 

  7. E.Hille, Functional analysis and semi-groups. Amer. Math. Soc. Col. Publ.31, New York, (1948).

  8. G. G. Lorentz, Majorants in spaces of integrable functions. Amer. J. Math.77, 484–492 (1955).

    Google Scholar 

  9. I. P.Natanson, Konstruktive Funktionentheorie. Berlin 1955.

  10. I. P.Natanson, Theorie der Funktionen einer reellen Veränderlichen. Berlin 1954.

  11. O. Perron, Über die Approximation stetiger Funktionen durch trigonometrische Polynome. Math. Z.47, 57–65 (1942).

    Google Scholar 

  12. E. S. Quade, Trigonometric approximation in the mean. Duke math. J.3, 529–543 (1937).

    Google Scholar 

  13. P. Romanovsky, Quelques considerations sur la théorie des intégrales singulières. Math. Z.34, 34–39 (1932).

    Google Scholar 

  14. Károly, Tandori, Über die Konvergenz singulärer Integrale. Acta Sci. math.15, 223–230 (1954).

    Google Scholar 

  15. C. de laVallée-Poussin, Sur l'approximation des fonctions d'une variable réelle et de leurs dérivées par les polynÔmes et des suites limitées de Fourier. Bull. Acad. Roy. de Belgique3, 193–254 (1908).

    Google Scholar 

  16. M. Zamansky, Classes de saturation de certains procédés d'approximation. Ann. Sci. Ec. norm. sup. III. Sér.,66, 19–93 (1949).

    Google Scholar 

  17. A. Zygmund, Smooth functions. Duke Math. J.12, 47–76 (1945).

    Google Scholar 

  18. A.Zygmund, Trigonometrical series. Warsaw 1935.

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  1. Mainz

    Paul L. Butzer

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  1. Paul L. Butzer
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Butzer, P.L. On the singular integral of de la Vallée-Poussin. Arch. Math 7, 295–309 (1956). https://doi.org/10.1007/BF01900307

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