Fourier Inversion Formula

This lecture covers the Fourier inversion formula, discussing the process of finding the inverse of a function using Fourier transforms. The instructor explains the mathematical concepts behind the formula and its applications, emphasizing the importance of understanding the sign. The lecture delves into the natural definition of the right-hand side of the formula and explores the continuity of the function. Various properties of the Schwartz space are introduced, including rapidly decreasing functions and the inclusion of Gaussians. The lecture concludes with a detailed proof of the formula, showcasing the convergence and continuity aspects. Special attention is given to the Schwartz space and its role in defining the inverse function.