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\begin{slide}
\rl{\tiny Rech, 19. 4. 2005}

\centerline{\textcolor{hegruen}{\Large\bf Green} }

\vskip -2mm {\tiny  
$$ \begin{tabular}{ c | c | c}  
      \hspace*{2cm}
      &\hspace*{1cm} Operator $L$ \hspace*{1cm}& 
       \hspace*{1.4cm} $G$ \hspace*{1.4cm}  
   \\[4pt] \hline  \rule[-2.2mm]{0pt}{9mm}
     (6.101) & $\dis \6_x$  
         &  $ \theta (x)$ 
   \\ \hline  \rule[-2.2mm]{0pt}{9mm}
     (7.40) & $\dis\6_t + \g $ 
         & $\dis \theta (t)\, {\rm e}^{-\g t}$  
   \\ \hline \rule[-2.2mm]{0pt}{9mm}
     & $\dis ( \6_t + \g )^2 $ 
       & $\dis \theta (t)\,t\, {\rm e}^{-\g t}$  
   \\[1mm] \hline \rule[-5mm]{0pt}{13mm}
  $\matrix{\hbox{1D harmon.~Osz.,} \cr
         \O\gll \wu{\o_0^2 - \g^2} \cr}$
     & $\dis \6_t^2 + 2\g\6_t + \o_0^2 $
       & $\dis \;\theta (t) {\rm e}^{-\g t} {1\0\O} \sin(\O t) $  
   \\ \hline  \rule[-5mm]{0pt}{13mm}
  Laplace, 2D & $\dis \D_2 = \6_x^2 + \6_y^2 $ 
       & $\dis {1\02\pi}\,\ln (\varrho ) $ 
   \\[3mm] \hline  \rule[-5mm]{0pt}{13mm}
  Laplace, 3D, (8.51) & $\dis \D = \6_x^2 + \6_y^2 + \6_z^2 $ 
       & $\dis {-1\0 4\pi r} $ 
   \\[3mm] \hline  \rule[-5mm]{0pt}{14mm}
  Helmholtz & $\dis \D + k^2 $ 
       & $\dis {- {\rm e}^{-{\rm i}kr} \0 4\pi r} $  
   \\[3mm] \hline  \rule[-6mm]{0pt}{15mm}
  Diffusion, (12.79) & $\dis \6_t - D\D $ & $\dis \theta(t)\,
       \Big( {1 \0 4\pi D t} \Big)^{\!{3\02}} {\rm e}^{- {r^2 \0 4Dt}}$  
   \\[3mm] \hline  \rule[-6mm]{0pt}{16mm}
  Box, (11.18), (11.28) & $\dis \Box = {1\0 c^2} \6_t^2 - \D $ 
       & $\dis { \d\( t- {r\0c} \) \0 4\pi r} $  \\[3mm] \hline 
\end{tabular} $$ } 

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\end{slide}
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