Definition of a simple characteristic for an elliptic operator

Question

Could one give a definition of a simple characteristic for an elliptic operator?

For example, I have an elliptic operator: \begin{equation} P(x,D) = \sum\limits_{|\alpha|=2m}a_{\alpha}(x)D^{\alpha} + R(x,D), \, x\in \Omega\subset \mathbb{R}^2, \end{equation} where $R(x,D)$ is an operator of degree less than $2m$.

How can I check that it's characteristics are simple? In particular, I don't understand the phrase: "complex characteristics are simple".

Answer 1

Treves -- Linear Partial Differential equations