All Fourier and Harmonic Analysis

This group gathers theorems from Fourier and harmonic analysis, the study of decomposing functions into sums or integrals of simple oscillating pieces. It covers the classical convergence and summability results, including Fejer's and Carleson's theorems on when a Fourier series recovers the original function, the Parseval and Plancherel identities relating a function to its transform, the Poisson summation formula linking a function's values to those of its transform, and further results on convolution and on the kernels used to build Fourier approximations.