Convergence of C(k)/|x| to delta(x) when C(k) becomes small?

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Guest

Posted: Wed Dec 13, 2006 4:37 pm

Dear all,

Let us set C(k)= Sqrt[2\Pi] k Exp[-2\Pi^2 k^2] for k>0. I've got the
function I(x) = C(k)/|x|. Intuitively, when k is big enough I(x)
approaches a Dirac as, for example, C(0.5) = 0.9*10^(-3), C(1) =
10^(- Cool

and C(1.5) = 10^(-19). I've checked it out numerically (with
Matlab) and it seems to work.

Is there a way to describe this in a more formal way, if not in
continuous, at least in the discrete case?
Cheers,
Carine.

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