# 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

Let g be another function in . We have

From this relation for

or

Applying Lebesgue dominanted convergence theorem for we get

Taking we have g(0)=1 and and as

we finally get

so