Periodic Functions: Integrals and Approximations

This lecture covers the topic of periodic functions, focusing on integrals and approximations. The instructor explains the concept of compact support, periodicity, and the approximation of functions using trigonometric polynomials. Various properties and inequalities related to periodic functions are discussed, along with the proof of certain theorems. The lecture emphasizes the importance of understanding the behavior of functions within a specific interval and the methods to approximate them effectively.