Prove FT²(f(x))=f(-x) for Fourier transform

[liorda]

Prove: $$FT^2(f(x))=f(-x)$$ where $$FT$$ is the Fourier transform.

I tried to change $$x$$ into $$-x'$$ but with no success.

Do I need to separate cases for even f and odd f?

 

[Dick]

You just need to realize that e.g., integral(exp(i*k*t1)*exp(i*k*t2)*dk) is proportional to delta(t1+t2).