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 $\displaystyle L^{2}[-\pi,pi]$

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- Nov 9th 2011, 11:59 AMChandru1Set of continuous functions dense in C[-pi,pi]
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 $\displaystyle L^{2}[-\pi,pi]$

- Nov 9th 2011, 10:25 PMCaptainBlackRe: Set of continuous functions dense in C[-pi,pi]
- Nov 9th 2011, 10:51 PMChandru1Re: Set of continuous functions dense in C[-pi,pi]
- Nov 10th 2011, 04:19 AMCaptainBlackRe: Set of continuous functions dense in C[-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

CB