Basic definition
$$ \hat{F}(f(t)) = \hat{f}(\omega) $$$$ \hat{f}(\omega) = \int^{\infty}_{-\infty} f(t) e^{i \omega t} d\omega $$$$ \hat{F}\left(a f_1(t) + b f_2(t) + c f_3(t) = 0\right) = a \hat{f}(\omega) + b \hat{f}(\omega) + c \hat{f}(\omega) = 0$$