Editing Projection-slice theorem (section)

== The projection-slice theorem in ''N'' dimensions ==
In ''N'' dimensions, the projection-slice theorem states that the
[[Fourier transform]] of the projection of an ''N''-dimensional function
''f''('''r''') onto an ''m''-dimensional [[Euclidean space|linear submanifold]]
is equal to an ''m''-dimensional slice of the ''N''-dimensional Fourier transform of that
function consisting of an ''m''-dimensional linear submanifold through the origin in the Fourier space which is parallel to the projection submanifold. In operator terms:

:<math>F_mP_m=S_mF_N.\,</math>