https://shiraz-k.com/tags/harmonic-analysis/ Recent content in Harmonic Analysis on Shiraz Hugo en-us Thu, 12 Dec 2024 13:02:50 +0530 https://shiraz-k.com/posts/harmonic-analysis/ Thu, 12 Dec 2024 13:02:50 +0530 https://shiraz-k.com/posts/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. https://shiraz-k.com/posts/fourier/ Mon, 02 Oct 2023 14:59:15 -0400 https://shiraz-k.com/posts/fourier/ 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.