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Math Help - inverse Fourier transform

  1. #1
    Junior Member
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    inverse Fourier transform

    How does one show that the inverse Fourier transform of e^-a|y|, a>0 is

    (a/pi)*1/(x^2+a^2)

    thanks!
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  2. #2
    MHF Contributor
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    Have you considered the definition of the Transform?
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  3. #3
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    Yes, but I'm confused about how to integrate e^-a|y|*e^-iyx to get that answer
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  4. #4
    A Plied Mathematician
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    I would probably use the equation

    |y|=\begin{cases}y,\quad &y\ge 0\\ -y,\quad &y<0\end{cases},

    and then split up your integral into two pieces depending on which of the two cases is applicable.
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