Hi All,(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to understand more rigorously why the Fourier transform of a constant functions equals the Dirac delta distribution.

I found somewhere this is justified by imposing the self-adjointness, so that under a duality pairing <..,..> and indicating withF(f) the transform of a function f, it is required that

<F(δ), g> = < δ ,g>

If g equals the constant unitary function my source, http://en.wikipedia.org/wiki/Dirac_delta_function#Fourier_transform, quotes,

<1,F(g)> = g (0)= < δ , g >

I understand the second equality, but not sure about the first...

Many thanks for your help

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# Fourier Trasform of Delta functions

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