[nkomal]

Hi I'm learning about Fourier series and I see how most of non constant functions do have a minimal period, do there exist some which don't?

and hw can it be proven that a continuous function does have a minimal period. Its pretty obvious for functions like sin and cosine, but not sure how it works otherwise.

thank you

[ebaines]

There are plenty of continuous functons that are not periodic, and hence do not have a period. Consider for example the identity function f(t)=t; this can't be represented by a Fourier series unless you limit the domain of values that "t" can take on. If you call that domain T, then the Fourier transform of f(t)=t becomes a series of "ramps" of width T, so that it becomes a "periodic" identity functon.