Fourier Transform: Schwartz Space

This lecture covers the Fourier transform on Schwartz space, emphasizing its properties such as being a continuous, linear bijection with an inverse Fourier transform. The instructor reviews the lemma on uniform limits of differentiable functions and highlights the density of smooth compactly supported functions in Schwartz space. The lecture progresses through the analysis of various slides, discussing the convergence of Riemann sums and the application of the Fourier transform to Schrödinger equations with initial data.