\begin{frame}
\begin{defi}
The class of symbols $\mathnormal{S^m}$ consist the set of
function $\mathnormal{ P(x,\xi)\in C^\infty(R^N\times R^N)}$ such
that for each compact set $\mathnormal {K\subset R^N}$ and
all multi-indices
$\alpha , \beta$ satisfying
$$\mathnormal{|D_x^\beta D_\xi^\alpha P(\xi)| \leq C_{\alpha ,\beta} (\big1+|\xi|)^{m-|\alpha|}}.$$
%where $|\alpha|=\alpha_1+\dots+\alpha_n $ , and $\mathnormal{m\in
\end{defi}
Formula (1) assigns to each symbol $\mathnormal{P(x,\xi)\in S^m}$
a pseudodifferential operator $\mathnormal{ P(x,D)}$ of order
$\mathnormal{m}.$ \newline
\textbf{Example}: The function $\mathnormal{p(\xi)=\sqrt{1+|\xi|^2}}$ is a pseudodifferential
symbol of order 1. Where $\mathnormal{\big1+|\xi|^2}$ is the
symbol of $1-\triangle$, and ${\triangle=\partial_{x_1}^2+\ldots +\partial_{x_n}^2}$ is Laplace operator.
\end{frame}
Thanks in advance for any help
\documentclass{...}and ending with\end{document}. – samcarter_is_at_topanswers.xyz Jul 31 '17 at 23:49\[ … \]preferable to$$? – samcarter_is_at_topanswers.xyz Jul 31 '17 at 23:50\bigyou are using (twice) without delimiter. – Sigur Jul 31 '17 at 23:51\mathnormal. – Sigur Aug 01 '17 at 00:07