- #1
Euge
Gold Member
MHB
POTW Director
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Here is this week's POTW:
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Let $D_n(t) = \sum\limits_{\lvert k\rvert \le n} e^{2\pi i kt}$ for $t\in [-.5, .5]$. Show that if $n \ge 2$, there are positive constants $A$ and $B$ independent of $n$, such that
$$A \le \frac{1}{\log n}\int_{-.5}^{.5} |D_n(t)|\, dt \le B$$
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Remember to read the https://mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to https://mathhelpboards.com/forms.php?do=form&fid=2!
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Let $D_n(t) = \sum\limits_{\lvert k\rvert \le n} e^{2\pi i kt}$ for $t\in [-.5, .5]$. Show that if $n \ge 2$, there are positive constants $A$ and $B$ independent of $n$, such that
$$A \le \frac{1}{\log n}\int_{-.5}^{.5} |D_n(t)|\, dt \le B$$
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Remember to read the https://mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to https://mathhelpboards.com/forms.php?do=form&fid=2!