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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- May 26th 2011, 05:42 PMmorganforinverse 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! - May 26th 2011, 07:49 PMTKHunny
Have you considered the definition of the Transform?

- May 27th 2011, 07:47 AMmorganfor
Yes, but I'm confused about how to integrate e^-a|y|*e^-iyx to get that answer

- May 27th 2011, 08:23 AMAckbeet
I would probably use the equation

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

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