Harmonic Analysis: Classical Theory and Fourier Series

This lecture introduces the harmonic analysis course, focusing on classical theory and Fourier series. The instructor explains the structure of the course, the importance of exercises, and the evaluation criteria. The lecture delves into harmonic analysis on the circle, discussing functions, continuity, and smoothness requirements. It explores the representation of functions using complex exponentials and the convergence of Fourier series. The instructor emphasizes the significance of Fourier series in various applications, such as PDEs, and the role of eigenfunctions of the Laplacian. The lecture concludes with a detailed proof of convergence results for Fourier series, highlighting the key ideas and techniques used in the analysis.