合成積と畳み込み積分
性質
$ ({\cal F}(x)*{\cal F}(y))(\omega)={\cal F}^{-1}\circ{\cal F}({\cal F}(x)*{\cal F}(y))(\omega)
$ = {\cal F}^{-1}(\omega\mapsto{\cal F}^2(x)(\omega){\cal F}^2(y)(\omega))(\omega)
$ {\cal F}(f)(\omega)=\int_\R f(t)e^{-i\omega t}\mathrm d t=2\pi{\cal F}^{-1}(f)(-\omega)だから
References
んん？定義が違う……