Is it possible to evaluate an inverse fourier transform of these functions?
$f(\omega)=\exp(-(k^2-\omega^2)^{1/2})$,
$g(\omega)=\frac{\exp(-(k^2-\omega^2)^{1/2})}{(k^2-\omega^2)^{1/2}}$,
where k is a constant.
Does the IFT exist for such a function? Are there methods by which one can approximate $f(\omega)$ and $g(\omega)$ using functions which have an inverse fourier transform and thereby obtain an approximate solution in real space?
It would be very helpful if anyone can provide some suggestions. Thank you!