I currently work on some Fourier transformations with mathematica and stumbled onto something strange while doing so.
I started a new kernel/notebook and entered
FourierTransform[Cos[p^2] Sin[p^2]/p, p, x]
The solution was
1/2 I Sqrt[\[Pi]/2] FresnelC[x/(2 Sqrt[\[Pi]])] -
1/2 I Sqrt[\[Pi]/2] FresnelS[x/(2 Sqrt[\[Pi]])]
and this seems right to me. In the next input I added an factor:
FourierTransform[Cos[a p^2] Sin[p^2]/(p), p, x]
Now the result was 0. If I assign a value to a, e.g. 1 or 2 I get a normal result but with a variable this transforms to zero. I also tried some Assumptions like making a real number or bigger then zero but nothing helped, the result is still zero.
Has anybody an idea why mathematica sais this Fourier transform is zero with a prefactor?
Thanks in advance
P.S.: I'm working with mathematica 18.104.22.168. and on SUSE 11.3