From https://news.ycombinator.com/item?id=25190770#25194040 :
> Convolution is in fact multiplication in Fourier space (this is the convolution theorem [1]) which says that Fourier transforms convert convolutions to products. 1. https://en.wikipedia.org/wiki/Convolution_theorem :
>> In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms.
"QFT and iQFT; Inverted Quantum Fourier Transform" https://en.wikipedia.org/wiki/Quantum_Fourier_transform