Newton polygons and parabolic inhomogeneous symbols of partial differential equations

When transforming PDE problems using Fourier and Laplace transforms, we can find functions that represent the problem, and which can be used to determine properties of the problem. We define such functions as symbols $P(\lambda,z)$. In general, we define the class of symbols $S(L_t\times L_x)$ are all functions which are represented by a...