commit 6ffdaa34151061534933d5573437f43ffa487ad9
parent d24466ffb9e7cd5a232f451ab62d271d5bb586af
Author: miksa234 <milutin@popovic.xyz>
Date: Fri, 13 Aug 2021 11:46:42 +0200
final, abgabe
Diffstat:
4 files changed, 3 insertions(+), 3 deletions(-)
diff --git a/pdfs/thesis.pdf b/pdfs/thesis.pdf
Binary files differ.
diff --git a/src/thesis/chapters/1_basics.tex b/src/thesis/chapters/1_basics.tex
@@ -292,7 +292,7 @@ space which takes out all the elements from the tensor product that don't
preserver the left/right representation and that are duplicates.
\begin{mydefinition}
Let $A$, $B$ be \textit{matrix algebras}. The \textit{Hilbert bimodule} for
- $(A, B)$ is given by an $A$-$B$-bimodue $E$ and by an $B$-valued
+ $(A, B)$ is given by an $A$-$B$-bimodule $E$ and by an $B$-valued
\textit{inner product} $\langle \cdot,\cdot\rangle_E: E\times E \rightarrow
B$, which satisfies the following conditions for $e, e_1, e_2 \in
E,\ a \in A$ and $b \in B$
@@ -304,7 +304,7 @@ preserver the left/right representation and that are duplicates.
\langle e_1,\ e_2\rangle_E &= \langle e_2,\ e_1\rangle^*_E \;\;\;\; &
\text{hermitian}, \\
\langle e,\ e\rangle_E &\ge 0 \;\;\;\; & \text{equality
- holds iff $e=0$}.
+ holds if and only if $e=0$}.
\end{align}
We denote $KK_f(A,\ B)$ as the set of all \textit{Hilbert bimodules} of $(A,\ B)$.
\end{mydefinition}
diff --git a/src/thesis/chapters/4_heatkernel.tex b/src/thesis/chapters/4_heatkernel.tex
@@ -104,7 +104,7 @@ kernel coefficients.
\subsubsection{Spectral Functions}
Manifolds $M$ with a disappearing boundary condition for the operator
-$e^{-tD}$ for $t>0$, i.e. a trace class operator on $L^2(V)$. Meaning for any
+$e^{-tD}$ for $t>0$, i.e.\ a trace class operator on $L^2(V)$. Meaning for any
smooth function $f$ on $M$ the Heat kernel can be defined as
\begin{align}
K(t,f,D) := \text{Tr}_{L^2}(fe^{-tD}).
diff --git a/src/thesis/main.pdf b/src/thesis/main.pdf
Binary files differ.
