Harmonic Analysis

The Fourier transform maps a complex-valued function to a function on its Pontryagin dual space. Generalizations of this concept to non-Abelian compact and locally compact Lie groups are reviewed.

The Fourier transform takes a function and outputs a different (possibly complex-valued) function. We also have something called the Fourier series, which takes a periodic function and gives a summation rather than an integral. I want to derive the Fourier series using the Fourier transform for anyone who is interested in connecting the two concepts with each other.