The Stone-Weierstrass Approximation Theorem and Applications

Title

The Stone-Weierstrass Approximation Theorem and Applications

Authors

Presenter(s)

Melissa E Fox, Emma Laura Whitney

Files

Description

Abstract: We outline the proof of the celebrated Stone-Weierstrass Theorem and give two applications. It is known that the polynomials are dense on C[a,b], the space of continuous functions defined on a closed bounded interval [a,b]; that is, given a continuous function and a tolerance for that function, a polynomial can be found within the tolerance of the function. We show that in the space C(M), where M is compact, if we consider the subalgebra A of C(M) that contains the constant functions and separates points of C(M), then A is dense in C(M). Then it follows that the piecewise linear functions and the trigonometric polynomials are dense in the space of continuous functions on compact domains.

Publication Date

4-5-2017

Project Designation

Capstone Project - Undergraduate

Primary Advisor

Paul W Eloe

Primary Advisor's Department

Mathematics

Keywords

Stander Symposium poster

The Stone-Weierstrass Approximation Theorem and Applications

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