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Bibliography
Bernstein, S., Démonstration du théorème de Weierstrass, fondée sur le calcul des probabilités,Commun. Soc. Math. Kharkow (2), 13 (1912-1913), 1–2.
Butzer, P. L., Linear combinations of Bernstein polynomials,Canadian Journal of Mathematics (1953), 559–567.
Butzer, P. L., Zur Frage der Saturationsklassen singulärer Integraloperatoren,Math. Zeit., 70 (1958), 93–112.
Courant, R. and Hilbert, D.,Methods of Mathematical Physics, New York, 1953.
de Leeuw, K., On the adjoint semigroup and some problems in the theory of approximation, to appear.
Dzyadyk, V. K., Constructive characterization of functions satisfying the condition Lip α on a finite segment of the real axis,Izv. Akad. Nauk. U.S.S.R., (1956), 623–642.
Favard, J., Sur l'approximation dans les espaces vectoriels,Annali di Matematica, 29 (1949), 259–291.
Kantorovitch, L. V., Sur certains developpements suivant les polynômes de la forme de S. Bernstein I, II,C. R. Acad. Sci. U.S.S.R. (1930), 563–568, 595–600.
Lorentz, G. G., Bernstein Polynomials, Toronto 1953.
Natanson, L. P., Konstruktive Funkionentheorie, Berlin, 1955.
Voronovskaya, E., Détermination de la forme asymptotique d'approximation des fonctions par les polynômes de M. Bernstein,C. R. Acad. Sci. U.S.S.R. (1932), 79–85.
Widder, D. V., The Laplace Transform, Princeton, 1946.
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This work was supported by the U.S. Air Force Office of Scientific Research.
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de Leeuw, K. On the degree of approximation by Bernstein polynomials. J. Anal. Math. 7, 89–104 (1959). https://doi.org/10.1007/BF02787682
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DOI: https://doi.org/10.1007/BF02787682