It is a well known fact that [tex]\int dk \tilde{F}(k) = F(0)[/tex] where the tilde denotes the Fourier transform. (take or leave some [tex]\pi[/tex]s) Is it possible to show this(adsbygoogle = window.adsbygoogle || []).push({});

1) without assuming that we know [tex]\int dx e^{ikx} = \delta(k)[/tex]

and 2) without saying: "well we know what the inverse Fourier transform looks like, so see what you evaluate if you put in a zero". (I think this would burn down to 1 anyways)

If the prove is impossible, can someone provide a link to a conclusive proof of the delta function property. Sorry if it looks like homework, it really isn't.

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# Integral over the fourier transform

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