Orthogonal Polynomials

This lecture covers the concept of L^2 bases and orthogonal polynomials, focusing on their properties and applications. The instructor explains how orthogonal polynomials form a basis in L^2 and their role in polynomial approximation. The lecture also delves into the conditions under which orthogonal polynomials exist and how they can be used to form a basis for certain spaces. The discussion extends to the analytical aspects of orthogonal polynomials, including their relationship with approximation theory and function spaces.