Compute the integral
by using Parseval's formula for Fourier transform
where means the Fourier transform of a function
Using Parseval's formula we can rewrite the integral as
with their inversions as follows
by the table 2 in Folland p.223
and the other one
which I calculated myslef as follows
we let and then the Fourier transform of g(x) is
then using formula in Folland again table 2
and applying it to our function
we get
going back to the integral and plugging in everything in the Parseval's formula gives me smth like this
in the solution given by our teacher we find
how did he get this on the left hand side and then on the right hand side??