[photonemitter]

There’s a theorem known as the Convolution Theorem: https://en.m.wikipedia.org/wiki/Convolution_theorem

Much used in simplifying kernel operations and convolutions (and some other nifty tricks.)

Another useful idea is also that in the domain of the fourier transformation we have exponentials (Fourier series are some series of $ c_n e^inx$), and when multiplying exponentials we get $ e^ix * e^iy = e^i(x + y) $

Moreover this is usually coupled with the case where we integrate on some periodic signal (so it’s integrated from 0 to 2pi, and unless the product of e^i(x+y) = e^0 = 1, then the integral becomes 0 as well. )