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arrow_back What does Wirtinger's Inequality state?

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What does  Wirtinger's Inequality  state?

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Wilhelm #Wirtinger was an Austrian mathematician born in 1865. One of his contributions is Wirtinger's Inequality, widely used in many areas of #Analysis. Notably, he also had some remarkable students like Gödel or Schrödinger.

Let $f: \mathbb{R} \rightarrow \mathbb{R} \in \mathcal{C}^{1}$ be a $(b-a)$ -periodical function. Then
$$
\begin{gathered}
\int_{a}^{b}|f(t)-c|^{2} d t \leq\left(\dfrac{b-a}{\pi}\right)^{2} \int_{a}^{b}\left|f^{\prime}\right|^{2} d t \\
\text { where } c=\dfrac{1}{b-a} \int_{a}^{b} f(t) d t
\end{gathered}
$$

 

by Platinum
(106,844 points)

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