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Theoreme de Müntz Pour les Fonctions de Plusieurs Variables

Published online by Cambridge University Press:  20 November 2018

Bernard H. Aupetit
Bernard H. Aupetit*
Affiliation:
Université Laval, Québec Québec
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Le théorème de Weierstrass affirme que toute fonction réelle continue sur l'intervalle [0, 1] est limite uniforme d'une suite de polynômes (voir [5]). Dans [4], Ch. Müntz généralise ce résultat de la façon suivante.

Soit α1, α2, α3,… une suite strictement croissante et non bornée de nombres réels.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 2 , June 1973 , pp. 165 - 166
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Achiezer, N.I., Theory of approximation, Ungar, New York (1956), 43–46.Google Scholar
2. Feller, William, On Miüntz' theorem and completely monotone functions, Amer. Math. Monthly, 75 (1968), 342–350.Google Scholar
3. Goffman, Casper and Pedrick, George, First course in functional analysis, Prentice-Hall, Englewood Cliffs, NJ. (1965), 181–182.Google Scholar
4. Müntz, Ch. H., Über den Approximationssatz von Weierstrass, Math. Abhandlungen H. A. Schwarz zu seinem 50. Doktorjubiläum gewidmet Berlin (1914), 303–312.Google Scholar
5. Stone, Marshall H., A generalized Weierstrass approximation theorem, Mathematical Association of America, M.A.A. Studies in Mathematics, Vol. 1, 30–87.Google Scholar