The convolution theorem states that the Fourier transform of the convolution of functions equals the pointwise multiplication of Fourier-transformed functions, i.e.:

$$\mathcal{F}\{f*g\} = \mathcal{F}\{f\} \cdot \mathcal{F}\{g\}$$

Are there other interesting $\mathcal{F}$ and $*$ for which the above holds, i.e. are there operations other than convolution that can be realized by pointwise multiplication, after some integral transform? I realize that 'interesting' is a bit vague, of course.

I understand that there are convolution theorems for Laplace and other similar transforms (under suitable conditions), but I'm unable find out about other operations and integral transforms.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.