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On the Müntz-Szász theorem for $ C[0,\,1]$


Author: Alan R. Siegel
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
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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 [Enhancements On Off] (What's this?)

  • [1] Ch. H. Müntz, Über den Approximationssatz von Weierstrass, H. A. Schwarz Festschrift, Berlin, 1914, pp. 303-312.
  • [2] 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
  • [3] Otto Szász, Über die Approximation stetiger Funktionen durch lineare Aggregate von Potenzen, Math. Ann. 77 (1916), no. 4, 482–496 (German). MR 1511875, https://doi.org/10.1007/BF01456964

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DOI: https://doi.org/10.1090/S0002-9939-1972-0306777-0
Article copyright: © Copyright 1972 American Mathematical Society