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Méthodes stochastiques pour la détermination de polynômes de Bernstein. (French) Zbl 0321.60065

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
41A10 Approximation by polynomials
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References:

[1] S. Bernstein , Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités . Commun. Soc. Math. Kharkow , t. 13 , n^\circ 2 , 1912 - 1913 , p. 1 - 2 . JFM 43.0301.03 · JFM 43.0301.03
[2] A.O. Gelfond , On the generalized polynomials of S . N. BERNSTEIN (en russe). Izv. Akad. Nauk SSSR, ser. math. , t. 14 , 1950 , p. 413 - 420 . MR 37945 | Zbl 0039.06803 · Zbl 0039.06803
[3] I.I. Hirschman et D.V. Widder , Generalized Bernstein Polynomials . Duke Math. J. , t. 16 , 1949 , p. 433 - 438 . Article | MR 30649 | Zbl 0033.11103 · Zbl 0033.11103
[4] S. Karlin et W.J. Studden , Tchebycheff Systems: with Applications in Analysis and Statistics , Interscience , New York , 1966 . MR 204922 | Zbl 0153.38902 · Zbl 0153.38902
[5] G.G. Lorentz , Bernstein polynomials . University of Toronto Press , Toronto , 1953 . MR 57370 | Zbl 0051.05001 · Zbl 0051.05001
[6] C. Muntz , Uber den Approximationssatz von Weierstrass . Mathematische Abhandlungen (Schwarzes Festschrift) , Berlin , Springer , 1914 , p. 303 - 312 . JFM 45.0633.02 · JFM 45.0633.02
[7] E. Parzen , Stochastic Processes Holden-Day San Francisco , 1962 . MR 139192 | Zbl 0107.12301 · Zbl 0107.12301
[8] L. Schwartz , Étude des sommes d’exponentielles réelles . Hermann , Paris , 1943 . Zbl 0061.13601 · Zbl 0061.13601
[9] G. Szego , Orthogonal Polynomials . Amer. Math. Soc. Colloquium. Publications , Vol. XXIII , Providence , 1939 . Zbl 0023.21505 | JFM 65.0278.03 · Zbl 0023.21505
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