Fourier transform of function times periodic function

[aaaa202]

Suppose I have a function of the type:

h(t) = g(t)f(t)

where g(t) is a periodic function. Are there any nice properties relating to the Fourier transform of such a product?

Edit: If not then what about if g(t) is taken as the complex exponential?

 

[DrClaude]

Not sure about your first question, but if
$$
h(t) \Leftrightarrow H(f)
$$
is a transform pair, then
$$
h(t) e^{-2 \pi i f_0 t} \Leftrightarrow H(f - f_0)
$$
and its called frequency shifting (taken from Numerical Recipes in C).