I've encountered problems of this type:
A potential can be written as V(r)=V(r+R) where R is a lattice vector. Show that V can be written as V(r)= sum( V_G exp(i G.r) )
While I do understand that if V(r) can be expressed as a Fourier series, we have translational symmetry,
I don't know how to proof that any function with translational symmetry can be expressed as a Fourier series.
Can you help?