View source for Locality principle

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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060270/l0602701.png" /> with variable coefficients, written in the form

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060270/l0602702.png" /></td> </tr></table>

can be represented, in an appropriate sense, in a neighbourhood of a point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060270/l0602703.png" /> as a sum

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060270/l0602704.png" /></td> </tr></table>

where the first term is an operator with constant coefficients, and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/l/l060/l060270/l0602705.png" /> 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>