Approximation Theory

This group gathers theorems about how closely an arbitrary function can be approximated by a simpler class of functions, such as polynomials or trigonometric sums, and how good that approximation can be made. It covers the foundational Weierstrass and Stone-Weierstrass approximation theorems, Bernstein's explicit polynomial construction, the Muntz-Szasz theorem on which power sequences suffice to approximate every continuous function, and further results, including Mergelyan's theorem on complex polynomial approximation, that extend the same questions to other settings.