Is the Plane Wave Decomposition of a Vector Field Accurate?

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Niles
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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.
 
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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.
 

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