Math 139 Fourier Analysis Lecture 17: Fourier Inversion

Fourier Inversion: creating an approximation of the identity using dilated Gaussians; convolution of Schwartz class functions; uniform convergence to the original function of the convolution of the approximation of the identity with the function. Fourier inversion formula: multiplication formula; inversion formula; inverse Fourier transform; Plancherel's theorem.