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Extending this principle to the case of an n-dimensional vector:
-Let $f$ be the periodic function expressed as $ f= \Sigma a_n \frac{1}{\sqrt{2\pi}} \, e^{inx} = \Sigma a_n \, f_n$ where $a_n \Epsilon \mathbb C$
+Let $f$ be the periodic function expressed as $ f= \Sigma a_n \frac{1}{\sqrt{2\pi}} \, e^{inx} = \Sigma a_n \, f_n$ where $a_n \in \mathbb C$
##Proving that this function is does indeed completely represent $f$