Topics in Fourier Analysis
A graduate-level introduction to Fourier analysis from MIT OpenCourseWare, covering five major topics in sequence. The course begins with Fourier series, including the Gibbs phenomenon and how convergence depends on the summation method used, then moves to the Fourier transform, developing the L1 theory before building the L2 theory through Hermite functions. It continues into Laurent Schwartz's theory of tempered distributions, then the weak convergence of probability measures and its application to deriving the Levy-Khinchine formula for infinitely divisible distributions. The final unit treats singular integral operators, starting with the Hilbert transform and using the method of rotations to establish Lp boundedness of even Calderon-Zygmund kernels. Materials include lecture notes and course structure typical of MIT OCW offerings, free to access, with no certificate attached.