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I'm having troubles with the Fourier transform of $f(x) = \frac{1}{1 +\|x\|^2} \in L^2(\mathbb{R}^{n})$. For the case $n=1$ I got $\hat{f}(\xi) = \pi e^{-2\pi |\xi|}$ using residues. Does the general case have a nice expression? How is that expression obtained?

Pipicito
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    Take a look here http://math.stackexchange.com/questions/472469/help-with-fourier-transform-integral?lq=1 – bcp Oct 05 '14 at 21:21
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    And here as well http://physics.stackexchange.com/questions/97784/integral-in-n%E2%88%92dimensional-euclidean-space – bcp Oct 05 '14 at 21:57
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    And the answer is probably here http://math.stackexchange.com/questions/662056/integral-in-n-dimensional-euclidean-space – bcp Oct 05 '14 at 22:21

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It's not in $L^2$ for $n \ge 4$. For $n \le 3$, assume wlog $\xi$ is in the direction of one of the coordinate axes.

Robert Israel
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