Mixing of a two signalsl in mixer

Since in mixer we multiplying two signals (periodic) in time domain, is this a convolution in frequency domain? How we can explain it ? Plz do guide me.

This is convolution in frequency domain.It is obtained from the principle of duality.
It is given by the formula,
x(t)y(t)

(X(

)*Y(

)).
The proof for this formula can be obtained easily.Hope this helps.