@@ -425,11 +425,13 @@ Let $X$ be a closed manifold and $E,F$ complex smooth vector bundles over $X$.

\end{enumerate}

\end{definition}

(see also \cref{def:diff_op-order-one,def:diff_op_general})

(see also \cref{def:diffop-first-order,def:diffop-general})

\begin{remark}

\begin{itemize}

\item First order differential operators suffice for many applications, for example \textcite{higson_roe} contend themselves with first order differential operators.

\item Computing the kernel of a differential operator amounts to solving a PDE.

\item First order differential operators suffice for many applications, for example \textcite[Def.~10.1.1]{higson_roe} content themselves with first order differential operators.

\item There are coordinate-free descriptions (using commutators with multiplication operators or jet bundles, see \cref{thm:diff_op_coordfree,sec:diffops_coordinate_independent_description}).