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Locality principle

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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 with variable coefficients, written in the form

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

where the first term is an operator with constant coefficients, and is "sufficiently small" in the given neighbourhood.

References

[1] N. Dunford, J.T. Schwartz, "Linear operators. Spectral theory" , 2 , Interscience (1963)
How to Cite This Entry:
Locality principle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Locality_principle&oldid=33394
This article was adapted from an original article by A.A. Dezin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article