Uniform convergent trigonometric series

If $f:[-\pi, \pi] \rightarrow\mathbb{C}$ is the value of an uniform convergent trigonometric series, can I then deduce that the $2\pi$-periodic normalized extension is an uniform convergent trigonometric series?

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 I am not sure whether the notation you use is totally standard. Well, even if it is I am pretty sure that people (like me) could answer your question if you made clearer what you mean by every word. – Simon Markett Jun 11 '12 at 11:33 The following is true: if a series $\sum_n (a_n \cos nx+b_n\sin nx)$ converges uniformly on $[-\pi,\pi]$, then it converges uniformly on $\mathbb R$. Whether or not this answers your question I can only guess. – user31373 Jun 11 '12 at 14:33