On the Müntz-Szász theorem for $C[0, 1]$
HTML articles powered by AMS MathViewer
- by Alan R. Siegel PDF
- Proc. Amer. Math. Soc. 36 (1972), 161-166 Request permission
Abstract:
The functions $1,{t^{{\lambda _1}}},{t^{{\lambda _2}}}, \cdots$ with complex $\lambda$’s are shown to be incomplete in $C[0,1]$ under conditions weaker than those proven by Szász, and a special construction due to P. D. Lax where the functions are complete is given.References
-
Ch. H. Müntz, Über den Approximationssatz von Weierstrass, H. A. Schwarz Festschrift, Berlin, 1914, pp. 303-312.
- Laurent Schwartz, Étude des sommes d’exponentielles. 2ième éd, Publications de l’Institut de Mathématique de l’Université de Strasbourg, V. Actualités Sci. Ind., Hermann, Paris, 1959 (French). MR 0106383
- Otto Szász, Über die Approximation stetiger Funktionen durch lineare Aggregate von Potenzen, Math. Ann. 77 (1916), no. 4, 482–496 (German). MR 1511875, DOI 10.1007/BF01456964
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 161-166
- MSC: Primary 41A30
- DOI: https://doi.org/10.1090/S0002-9939-1972-0306777-0
- MathSciNet review: 0306777