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On Weighted Polynomial Approximation With Gaps

Published online by Cambridge University Press:  11 January 2016

Guantie Deng
Guantie Deng*
Affiliation:
Department of Mathematics, Beijing Normal University, 100875 Beijing, The People’s Republic of China, [email protected]
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Abstract

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Let α be a nonnegative continuous function on ℝ. In this paper, the author obtains a necessary and sufficient condition for polynomials with gaps to be dense in Cα, where Cα is the weighted Banach space of complex continuous functions ƒ on ℝ with ƒ(t) exp(−α(t)) vanishing at infinity.

Keywords

30B6041A30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 178 , 2005 , pp. 55 - 61
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[1] Boas, R. P. Jr., Entire Functions, Academic Press, New York, 1954.Google Scholar
[2] Borichev, A., On weighted polynomial approximation with monotone weights, Proc. Amer. Math. Soc., 128 (2000), no. 12, 3613–3619.Google Scholar
[3] Borichev, A., On the closure of polynomials in weighted space of functions on the real line, Indiana Univ. Math. J., 50 (2001), no. 2, 829–845.Google Scholar
[4] Borwein, P. B. and Erdèlyi, T., Polynomials and Polynomial Inequalities, Springer-Verlag, New York, N. Y., 1995.CrossRefGoogle Scholar
[5] Branges, L. de, The Bernstein problem, Proc. Amer. Math. Soc., 10 (1959), 825–832.CrossRefGoogle Scholar
[6] Hall, T., Sur l’approximation polynōmiale des fonctions continues d’une variable réelle, Neuvième Congrès des Mathémticiens Scandianaves (1938), Helsingfors (1939), pp. 367–369.Google Scholar
[7] Izumi, S. and Kawata, T., Quasi-analytic class and closure of {tn} in the interval (-∞,∞), Tōhoku Math. J., 43 (1937), 267–273.Google Scholar
[8] Malliavin, P., Sur quelques procédés d’extrapolation, Acta Math., 83 (1955), 179–255.CrossRefGoogle Scholar
[9] Rockafellar, R., Convex analysis, Princeton Univ. Press, Princeton, 1970.CrossRefGoogle Scholar