Is the Plane Wave Decomposition of a Vector Field Accurate?

[Niles]

Hi

When we decompose e.g. the vector potential A into a sum of plane waves, then is it correct to say that we are describing an arbitrary vector field A, since we have decomposed it into its Fourier (= plane wave) components?Niles.

 

[Andy Resnick]

I'm sure there are some restrictions- I don't think *all* functions can be written as a converging Fourier series. I don't know what the official rules are, tho.