Hello and thanks for reading.
I have the next problem, which must solve with convolution property of Fourier transform.
Let be $f(t)=\sin(2t)\exp(-3|t|)$, and I meet the next Fourier transforms;
If $g(t)=\exp(-3|t|)$, so $\hat{g}(\omega)=\frac{6}{9+\omega^2}$ And
If $h(t)=\sin{2t}$, so $\hat{h}(\omega)=-i\pi(\delta(\omega-+2)-\delta(\omega-2))$
The answer is $\frac{-24i\omega}{\omega^4+10\omega+169}$, I got it with the definition.
The definition that we use in class is:
$\hat{f}(\omega)=\int^\infty_{-\infty}f(t)\exp{(-i\omega t)}dt$
The problem is correct multiply by Dirac delta out an integral? If the answer is yes, how I can it?