The Stone-Weierstrass Approximation Theorem and Applications
Melissa E Fox, Emma Laura Whitney
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.
Capstone Project - Undergraduate
Paul W Eloe
Primary Advisor's Department
Stander Symposium poster
"The Stone-Weierstrass Approximation Theorem and Applications" (2017). Stander Symposium Posters. 1118.