\documentclass{amsart}
\usepackage[slovene]{babel}
\begin{document}
\thispagestyle{empty}
\begin{table}[ht]
\caption{Lapaceova transformacija elementarnih funkcij}
\centering
\begin{tabular}{|r|lll||r|lll|}
\hline &&&&&&&\\
&$f(t)$&$F(s)$&&&$f(t)$&$F(s)$&\\[1ex]
\hline\hline &&&&&&&\\
1&$\displaystyle H(t)$&$\displaystyle \frac{1}{s}$&&2&$\displaystyle t^n$&$\displaystyle\frac{n!}{s^{n+1}}$&\\[2ex]
3&$e^{at}$&$\displaystyle\frac{1}{s-a}$&$s>a$&
4&$\displaystyle H(t-a)$&$\displaystyle\frac{1}{s}e^{-at}$&$a>0$\\[2ex]
5&$\displaystyle\sin(at)$&$\displaystyle\frac{a}{s^2+a^2}$&&
6&$\displaystyle\cos(at)$&$\displaystyle\frac{s}{s^2+a^2}$&\\[2ex]
7&$\displaystyle te^{at}$&$\displaystyle\frac{1}{(s-a)^2}$&$s>a$&
8&$\displaystyle t\sin(at)$&$\displaystyle\frac{2as}{(s^2+a^2)^2}$&\\[2ex]
9&$\displaystyle t\cos(at)$&$\displaystyle\frac{s^2-a^2}{(s^2+a^2)^2}$&&
10&$\displaystyle \frac{1}{2}\left(\sin(at)-at\cos(at)\right)$&$\displaystyle\frac{a^3}{(s^2+a^2)^2}$&\\[2ex]
11&$\displaystyle\delta(t)$&$\displaystyle 1$&&
12&$\displaystyle\delta(t-a)$&$\displaystyle e^{-as}$&$a>0$\\[1ex]
\hline
\end{tabular}
\end{table}
\vspace{-5mm}
\begin{table}[!ht]
\caption{Lapaceova transformacija pravila}
\centering
\begin{tabular}{|r|lll|}
\hline &&&\\
&$f(t)$&$F(s)$&\\[1ex]
\hline\hline &&&\\
i&$\displaystyle af(t)$&$\displaystyle aF(s)$&\\[1ex]
ii&$\displaystyle f(t)+g(t)$&$\displaystyle F(s)+G(s)$&\\[1ex]
iii&$\displaystyle f(at)$&$\displaystyle\frac{1}{a}F(\frac{s}{a})$&$a>0$\\[1ex]
iv&$\displaystyle H(t-a)f(t-a)$&$\displaystyle e^{-as}F(s)$&$a>0$\\[1ex]
v&$\displaystyle e^{at}f(t)$&$\displaystyle F(s-a)$&$s>a$\\[1ex]
vi&$\displaystyle f'(x)$&$\displaystyle sF(s)-f(0)$&\\[1ex]
vii&$\displaystyle f^{(n)}(t)$&\multicolumn{2}{l|}{$\displaystyle s^nF(s)-s^{n-1}f(0)-s^{n-2}f'(0)-\cdots-f^{n-1}(0)$}\\[1ex]
viii&$\displaystyle tf(t)$&$\displaystyle -F'(s)$&\\[1ex]
ix&$\displaystyle t^nf(t)$&$\displaystyle (-1)^nF^{(n)}$&\\[1ex]
x&$\displaystyle\int_0^tf(\tau)\,d\tau$&$\displaystyle\frac{1}{s}F(s)$&\\[2ex]
xi&$\displaystyle\frac{1}{t}f(t)$&$\displaystyle\int_s^\infty F(\sigma)\,d\sigma$&\\[1ex]
xii&$\displaystyle\int_0^tf(\tau)g(t-\tau)d\tau$&$\displaystyle F(s)G(s)$&\\[2ex]
\hline &&&\\
xiii&$\displaystyle f(0)=\lim_{s\to\infty}\left(sF(s)\right)$&
$\displaystyle \lim_{t\to\infty}f(t)=\lim_{s\to0}\left(sF(s)\right)$&\\[2ex]
\hline
\end{tabular}
\end{table}




\end{document}
