Period length of product of two periodic function, Fourier Series

[keenPenguin]

Hello,

I am currently dealing with Fourier Series, and a question about the period length of a product of two periodic functions is bothering me. If you have two different periodic functions with different (or the same) period and you sum them up, what happens to the period? Can this generally be said? Also (and this is what I'm especially interested in), what happens to the period of the product of these functions?

Another question: Fourier coefficients, no matter if real or complex, all go over any periodic interval of a function. Actually what happens if you (deliberately) chose an interval which is two times or three times the period? Does it (generally) still work?

kP

 

[estro]

Pardon me for archeological tendencies but I found this question very relevant:

Hello,
...
If you have two different periodic functions with different (or the same) period and you sum them up, what happens to the period? Can this generally be said? Also (and this is what I'm especially interested in), what happens to the period of the product of these functions?
...

I got feeling that period for product of periodic functions is the bigger period among the two functions, but I was unable to prove it.

I'm only interested on product of functions. [For sum of functions I waas able to prove the needed properties]