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The effect of a 2pi periodic function f is defined as

[tex] P(f) = 1/(2\pi) \int_{-\pi}^\pi |f(t)|^2 \ dt[/tex]

and Parsevals Theorem tells us that

[tex] P(f) = \sum_{n=\infty}^\infty |c_n|^2 [/tex]. Now, it seems rather intuituve that the effect of the N'te partial sum is

[tex] P(Sn) = \sum_{n=-N}^N |c_n|^2 [/tex] But what is the in-between math argument? And furthermore, how can i proove that the inequality [itex] P(Sn)/P(f) \geq \delta [/itex] is satisfied only if

[tex] \sum_{|n|>N} |c_n|^2 \leq (1-\delta)P(f) [/tex]

Thanks

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# Homework Help: Regarding approximation theorem

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