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A collective concept that combines a number of assertions related mainly to elliptic (in some cases to hypo-elliptic) equations (operators) and that follows from the pointwise character of the singularity of a fundamental solution for this class of equations. For example, an elliptic operator $L(D,x)$ with variable coefficients, written in the form

$$L(D,x)\equiv\sum_{|\alpha|\leq m}a_\alpha(x)D^\alpha,\quad x\in\mathbf R^n,$$

can be represented, in an appropriate sense, in a neighbourhood of a point $x_0$ as a sum

$$L(D,x)=\sum_{|\alpha|\leq m}a_\alpha(x_0)D^\alpha+L'(x),$$

where the first term is an operator with constant coefficients, and $L'(x)$ is  "sufficiently small"  in the given neighbourhood.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  N. Dunford,   J.T. Schwartz,   "Linear operators. Spectral theory" , '''2''' , Interscience  (1963)</TD></TR></table>