Inverse of Fourier transform
Submitted by Structure on Sat, 05/15/2010 - 06:57.
Let be the Fourier transform of a function f in
. We shall prove that
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Let g be another function in . We have
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From this relation for
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or
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Applying Lebesgue dominanted convergence theorem for we get
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Taking we have g(0)=1 and
and as
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we finally get
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so
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