Article
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:
[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.