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Symbolic 3D FourierTransform

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Hi everybody! 
I have a problem with the comand "FourierTransform[expr,{x,y,z},{kx,ky,kz}]". If i write expr as a generic funtion (like f[x,y,z]) the command doesn't return a generic function as results, but "FourierTransform[f[x,y,z],{x,y,z},{kx,ky,kz}]", while in the 1D if i input the comand FourierTransform[f,x,k] gives f! Why?
Thank you.
POSTED BY: Pietro Zaccagnini
Answer
10 months ago
For the 1D case, you didn't make f a function of x.  In the 3D case, the function returns unevaluated as it has no rule to handle that case.
POSTED BY: Frank Kampas
Answer
10 months ago
To Frank Kampas: I forgot to write "". I meant that in the 1D case it returns me the function in the new dominium.. I'm sorry for misunderstanding
POSTED BY: Pietro Zaccagnini
Answer
9 months ago
Here is an example of 3D symbolic Fourier transformation asymmetric in variables:
In[] = FourierTransform[x y^2 z^3 Exp[-(x^2 + z^2 + y^2)], {x, y, z}, {u, v, w}]
Out[] = -((E^(-(u^2/4) - v^2/4 - w^2/4)*u*(-2 + v^2)*w*(-6 + w^2))/(128*Sqrt[2]))
POSTED BY: Sam Carrettie
Answer
10 months ago
Thank you, but i meant something like that:
FourierTransform[f[x,y,z],{x,y,z},{kx,ky,kz}]

where f[x,y,z] is one of some unknown functions of a differential problem. I would like to transform the whole equations in the Fourier dominium to avoid the system of partial differential equations that i really don't know how to solve.

Thank you guys emoticon
POSTED BY: Pietro Zaccagnini
Answer
9 months ago
If I understand what you're trying to do, you should note that FourierTransform[f[x,y,z],{x,y,z},{kx,ky,kz}] does return a function of kx,ky, and kz, even if it remains in that form. That is, running the following code
Ff[kx_, ky_, kz_] :=
FourierTransform[f[x, y, z], {x, y, z}, {kx, ky, kz}];
InverseFourierTransform[Ff[kx, ky, kz], {kx, ky, kz}, {x, y, z}]

correctly returns f[x,y,z]. I'd presume then you can work with the Fourier transform symbolically, but it seems more practical to just use DSolve or NDSolve if you're solving a system of PDEs.
Answer
9 months ago
Thank you Humberto! I tried to use DSolve but its output is the command itself (I don't have boundary conditions), thats why I'm trying to solve the system in the Fourier's dominium. 
POSTED BY: Updating Name
Answer
9 months ago