From 12f9400b18b016767ae2b26bff43226807f6156d Mon Sep 17 00:00:00 2001 From: Jannes Bantje Date: Thu, 5 Mar 2020 10:01:44 +0100 Subject: [PATCH] fix a typo --- contents/coarse.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/contents/coarse.tex b/contents/coarse.tex index 98f0ac6..7f33142 100644 --- a/contents/coarse.tex +++ b/contents/coarse.tex @@ -90,7 +90,7 @@ The next main player of coarse index theory is the so-called \emph{localisation In the same setting as above we now look at the family $\varphi \enbrace*{\frac{1}{t} D}$ for $t \in [1,\infty)$.\todo{in what sense is this \enquote{local}?} If $\supp \widehat{\varphi} \subseteq (-r,r)$ we once again get $- \varphi \enbrace*{\frac{1}{t} D} = \frac{1}{\sqrt{2 \pi_n}} \int\limits_{-r}^r \widehat{\varphi}(\xi) e^{i \xi \frac{1}{t} D} \, \mathd \xi = \frac{1}{\sqrt{2 \pi_n}} \int\limits_{-r/t}^{r/t} \widehat{\varphi}(t \cdot \eta) e^{i \xi \eta D} \, \mathd \xi + \varphi \enbrace*{\frac{1}{t} D} = \frac{1}{\sqrt{2 \pi}} \int\limits_{-r}^r \widehat{\varphi}(\xi) e^{i \xi \frac{1}{t} D} \, \mathd \xi = \frac{1}{\sqrt{2 \pi}} \int\limits_{-r/t}^{r/t} \widehat{\varphi}(t \cdot \eta) e^{i \xi \eta D} \, \mathd \xi$ \begin{definition} -- 2.26.2