The symbol of differential operator has a confusing definition as a "polynomial" it is
$$\sigma_P(x,\xi) := \Sigma_{|\alpha|= k} P_\alpha(x)\xi^\alpha$$
So what is $\xi^{(1,2)}? $ Is it the polynomial $\xi_1\xi_2?$
Page 6 line 7, also, what is the definition of
$$(A^t(\tilde{x}) \xi)^\alpha $$ Equivalently, for a fixed matrix $A$, what is $$ (A \xi)^\alpha $$