KF Riley problem 13.7

Mathematics Asked by user215736 on October 4, 2020

Find the Fourier transform of the unit rectangular distribution
f(t)=1 |t|<1
0 otherwise
Determine the convolution of f with itself and, without further integration, deduce its transform.
Deduce that
mathint_{-inf}^{inf} frac{sin^2(w)}{w^2} = pimath

I obtained the Fourier transform of f and the convulation with itself but cannot use it to evaluate te integral. The problem is from KF Riley- 13.7

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