I have a function, f, in $L_1(R)$. I need to establish the following fourier transforms and I don't know how to do so. Can anyone guide me through one of these that would then help me get the other ones?
If $ g(x) = f(x + h)$ then $\hat g(\xi) = \hat f(\xi)e^{2\pi ih\xi}$ for any $h \in R$
If $g(x) = f(\delta x)$ then $\hat g(\xi) = \delta^{−1} \hat f (\delta^{−1} \xi)$ for any $\delta > 0$.