A survey on the Weierstrass approximation theorem

Abstract

The celebrated and famous Weierstrass approximation theorem characterizes the set of continuous functions on a compact interval via uniform approximation by algebraic polynomials. This theorem is the first significant result in Approximation Theory of one real variable and plays a key role in the development of General Approximation Theory. Our aim is to investigate some new results relative to such theorem, to present a history of the subject, and to introduce some open problems.

16 pages

References in corpus (1)

• On Hilbert extensions of Weierstrass' theorem with weights

Cited by in corpus (4)

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• An Identity for Two Integral Transforms Applied to the Uniqueness of a Distribution via its Laplace-Stieltjes Transform
• On Hilbert extensions of Weierstrass' theorem with weights
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