How do i show that the set of continuous functions in $\displaystyle C[-\pi,\pi] $ which are periodic, that is $\displaystyle f(+\pi)=f(-\pi)$ is dense in $\displaystyle L^{2}[-\pi,pi]$
Googleing for "l2 convergence of fourier series" will give you several PDFs which discuss this, alternativly follow the links in the Norm Convergence area of the Wikipedia page:
Convergence of Fourier series - Wikipedia, the free encyclopedia
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