Can Mathematica substitute for a Fourier transform table? That is, can it find the transform in ω of an unknown arbitrary function in x? The attached notebook contains examples of expressions that are resolved and expressions that are not resolved. They all come straight from the first few lines of a Fourier transform table. So I suspect I may be doing something wrong.
Thanks, Ted Ersek. That's right. When I posted the question, I had mistakes in the arguments that I corrected later. Mathematica does work as a super substitute for a table. There might be an exception though. I'm not sure if I'm making a mistake or if Mathematica doesn't resolve a convolution like the attached example.
Evaluate
InverseFourierTransform[ FourierTransform[g[x],x,\[Omega]] FourierTransform[f[x],x,\[Omega]], \[Omega],x]
and you get back just what you typed. For the other examples you asked about, Mathematica returns the result predicted in text books.
