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Symbolic 3D FourierTransform

Posted 11 years ago
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.
6 Replies
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.
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. 
Thank you, but i meant something like that:

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
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
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
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
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