I would like to compute the following iterated integral in 3 dimesions: $$ \int_{-\infty}^\infty \int_{-\infty}^\infty \left|\int_{-\infty}^\infty f(y)f(y-t)e^{-i 2 \pi t \xi} dy\right|dt d\xi $$ where $f$ is the spheroidal wave function which I can sample at arbitrary points using SpheroidalPS[].
The absolute value in the inner integral is the cause of the problem. What is the way of using NIntegrate to handle this absolute value for multiple integrals.
EDIT The requested code gives warnings
NIntegrate[Abs[NIntegrate[
SpheroidalPS[0, 0, Pi, y] SpheroidalPS[0, 0, Pi, y - t] Exp[-I 2 Pi t e],
{y, -Infinity, Infinity}]], {t, -Infinity, Infinity},
{e, -Infinity, Infinity}]
(*NIntegrate::inumr: The integrand ((-I) \[Infinity]) SpheroidalPS[0,0,\
[Pi],y] SpheroidalPS[0,0,\[Pi],-\[Infinity]] has evaluated to non-numerical
values for all sampling points in the region with boundaries {{-\
[Infinity],0.}}.*)