The properties derived for the Fourier transform apply to the Fourier series.
In particular, for two signals 
and 
with Fourier series 
and 
with the same ifundamental period, the convolution of 
and 
has a Fourier series 
.
Note that when the signal is even, the sine terms of the Fourier series are zero while if the signal is odd, the cosine terms are zero.