Thread: 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!

Have you considered the definition of the Transform?

Yes, but I'm confused about how to integrate e^-a|y|*e^-iyx to get that answer

I would probably use the equation



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