Commit f1582107 authored by Jannes Bantje's avatar Jannes Bantje

fixed index

parent 3c1c3f51
......@@ -282,7 +282,7 @@ In particular one proves, that this multiplication operator extends to a bounded
This is \cite[Prop.~3.3.3]{ebert_index_lec}.
The proof of Gårding's inequality is performed in three stages: firstly it is proven for differential operators with contants coefficients, then extended to variable coefficients with small support and from that the general case is deduced.\todo{how does the ellipticity come in?}
Another important tool, which will be useful in other places as well, are \Index{Friedrichs' mollifiers}:
Another important tool, which will be useful in other places as well, are \emph{Friedrichs' mollifiers}:
Let $\phi \in C^\infty_c(\mathbb{R}^n)$ be a function with $\phi \ge 0$, $\int \phi(x) \intmathd x = 1$ and $\phi(-x)=\phi(x)$.
For $\varepsilon>0$ we let $\phi_\varepsilon(x) = \frac{1}{\varepsilon^n} \phi \enbrace*{\frac{x}{\varepsilon}}$.
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