Inequality (Complex Analysis)
- From: Eliza <prelim_questions@xxxxxxxxx>
- Date: Fri, 29 Jun 2007 19:06:58 -0700
I tried asking this elsewhere without success. It has been bothering
me for awhile:
If f(theta) is a real-analytic function with period 2pi, show there
exists numbers a>0 and M>0 such that for all N,
| \int_0^{2\pi} f(\theta) d\theta - \frac{2 \pi}{N} \sum_{n=1}^N
f(\frac{2 \pi n}{N}) | \leq M \exp^{-a N}
where the bars of course represent absolute value.
Also, is this a well-known result? Where might I read more?
.
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