Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Can someone explain this step in the proof of the convolution theorem?

  1. Jun 17, 2011 #1
    I fail to understand a step made in this proof:
    http://en.wikipedia.org/wiki/Convolution_theorem" [Broken]

    more specifically the last step where the integral is written as a product of 2 seperate integrals (each equal to a fourier transform):
    I'm quite rusty on my integration, but as far I can remember this operation is only allowed when y is independent of x. (since y is taken out of an integral over x). But since we substituted y = z − x this is not the case. Can somebody explain me why this step is correct? (and why I'm wrong)
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jun 17, 2011 #2
    After the substitution, y is just a dummy variable and consequently independent of x. If it was a definite integral, the substitution would have moved the dependency on x to the integral limits but because the integral is over all space, they are still independent of x after the substitution.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook