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Keywords:
approximation by polynomials
Summary:
In the paper a simple proof of the Weierstrass approximation theorem on a function continuous on a compact interval of the real line is given. The proof is elementary in the sense that it does not use uniform continuity.
References:
[1] B. Brosowski, F. Deutsch: An elementary proof of the Stone-Weierstrass theorem. Proc. Am. Math. Soc. 81 (1981), 89–92. DOI 10.1090/S0002-9939-1981-0589143-8 | MR 0589143
[2] D. Jackson: A proof of Weierstrass’s theorem. Am. Math. Mon. 41 (1934), 309–312. DOI 10.2307/2300993 | MR 1523090 | Zbl 0009.15802
[3] H. Kuhn: Ein elementarer Beweis des Weierstrasschen Approximationsatzes. Arch. Math. 15 (1964), 316–317. DOI 10.1007/BF01589203 | MR 0173738
[4] E. Landau: Über die Approximationen einer stetigen Funktion durch eine ganze rationale Funktion. Palermo Rend. 25 (1908), 337–345.
[5] I. P. Natanson: Theory of Functions of a Real Variable (Engl. transl.) Vol 1. Ungar, New York, 1974. MR 0354979
[6] M. H. Stone: A generalized Weierstrass approximation theorem. Stud. Math. 1 (1962), 30–87. Zbl 0147.11702
[7] Béla Sz.-Nagy: Introduction to Real Functions and Orthogonal Expansions. Akadémiai Kiadó, Budapest, 1964. MR 0181711
[8] K. Weierstrass: Mathematische Werke. Preussische Akademie der Wissenschaften, 1903.
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