Are Fourier Series centered around a point like a Taylor series?

Question

If not, why? Is it usual for representations to have a center?

Answer 1

The notion of "centered around a point" applies for Taylor series, because it is a power series. Power series have a circle of convergence and thus some kind of center. But in the case of Fourier series you essentially consider a periodical function. There is no "special" point there.