Question

I need help on Fourier Transform...Anyone?
Suppose function g(x,y) with Fourier Transform G(kx, ky) [ie.,g(x,y) <=> G(kx,ky)] satisifies Laplace's Equation => d^2g/dx^2 + d^2g/dy^2 + d^2g/dz^2 = 0 for the z-dimension directed normal to the (x,y)-plane. Find the Fourier Transform pair for its first derivative with respect to x, then y, and z; then 2nd derivative w.r.t x, then y, then z; then 2nd derivative w.r.t. x and y, x and z, and y and z.

Answer 1

\[\nabla g = k \nabla G\]
\[\nabla^2 g = k \nabla^2 G = 0\]
\[\frac{∂ g}{∂z} = \frac{∂ G}{∂z} = 0 \]

Answer 2

I do not understand the implication of z-dimension being directed normally...i.e, the mathematical expression of that...plus how to prove a 2-D FT satisfies a 3D LE...basically the whole qstn...any help..big medals..new to the site..though..thanks