 Theorems in approximation theory

In approximation theory, several theorems provide fundamental insights into how functions can be approximated by simpler functions, such as polynomials, trigonometric series, or other basis functions. Here are some key theorems and concepts in approximation theory: 1. **Weierstrass Approximation Theorem**: This theorem states that any continuous function defined on a closed interval can be uniformly approximated as closely as desired by a polynomial function.