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author | LordMcFungus <mceagle117@gmail.com> | 2021-03-22 18:05:11 +0100 |
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committer | GitHub <noreply@github.com> | 2021-03-22 18:05:11 +0100 |
commit | 76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7 (patch) | |
tree | 11b2d41955ee4bfa0ae5873307c143f6b4d55d26 /vorlesungen/slides/2/funktionenraum.tex | |
parent | more chapter structure (diff) | |
parent | add title image (diff) | |
download | SeminarMatrizen-76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7.tar.gz SeminarMatrizen-76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7.zip |
Merge pull request #1 from AndreasFMueller/master
update
Diffstat (limited to '')
-rw-r--r-- | vorlesungen/slides/2/funktionenraum.tex | 70 |
1 files changed, 70 insertions, 0 deletions
diff --git a/vorlesungen/slides/2/funktionenraum.tex b/vorlesungen/slides/2/funktionenraum.tex new file mode 100644 index 0000000..f7733cc --- /dev/null +++ b/vorlesungen/slides/2/funktionenraum.tex @@ -0,0 +1,70 @@ +% +% funktionenraum.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Funktionenraum} +\vspace{-15pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{block}{Supremum-Norm} +Vektorraum +\[ +C([a,b]) += +\{f\colon[a,b]\to\mathbb{R}\;|\; \text{$f$ stetig}\} +\] +\only<2->{wird Banachraum }% +mit der Norm +\(\displaystyle +\|f\| += +\|f\|_{\infty} += +\sup_{x\in[a,b]} |f(x)| +\) +\end{block} +\uncover<3->{% +\begin{block}{$L^1$-Norm} +Vektorraum +\[ +L^1([a,b]) += +\{f\colon[a,b]\;|\;\text{$f$ integrierbar}\} +\] +\only<4->{wird Banachraum }% +mit der Norm +\[ +\|f\|_1 += +\int_a^b |f(x)|\,dx +\] +\end{block}} +\end{column} +\begin{column}{0.48\textwidth} +\uncover<5->{% +\begin{block}{$L^2$-Norm} +Vektorraum +\[ +L^2([a,b]) += +\{f\colon[a,b]\to\mathbb{R}\;|\; \|f\|_2^2<\infty\} +\] +mit Skalarprodukt +\begin{align*} +\langle f,g\rangle +&= +\int_a^b \overline{f}(x)g(x)\,dx +\\ +\|f\|_2^2 +&= +\int_a^b |f(x)|^2\,dx +\end{align*} +\uncover<6->{ist ein Banachraum} +\end{block}} +\end{column} +\end{columns} +\end{frame} |