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Fourier Transforms: Proving operational properties

  1. Oct 23, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    I wish to prove the following property of a Fourier transform:
    F(f)(x) = F^{-1}(f)(-x),
    which means that the Fourier transform of a function f in the x-variable is equal to the inverse Fourier transform in the -x-variable. This is proven here:

    http://www.sunlightd.com/Fourier/Duality.aspx [Broken]

    Now I wish to prove the following:
    F(f)(-x) = F^{-1}(f)(x),
    but I cannot get started. I am not sure of what substitutions to make. Can you give me a hint?

    Thanks in advance,

    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Oct 23, 2008 #2


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    If the first formula holds for any y, then just take x = -y. That's just it, isn't it?
  4. Oct 23, 2008 #3
    I guess you are right. Thanks :-)
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