I'm supposed to calculate : $ F[\delta(x-a)](\nu)F[e^{i2\pi \nu x}](\nu)$
Since $F[\delta(x-a)] = e^{i 2\pi \nu a}F[\delta(x)] = e^{i 2\pi \nu a}$
it leaves : $$e^{i 2\pi \nu a}F[e^{i 2\pi \nu x}] = e^{i 2\pi \nu a}\int_{-\infty}^{\infty}e^{i 2\pi \nu x}e^{-i 2\pi \nu x}dx = e^{i 2\pi \nu a}\int_{-\infty}^{\infty}dx$$
which does not converge...
So what am I doing wrong ?