Fundamental solution

Summary

A fundamental solution of a linear differential operator $P$ is a distribution $E$ with $P E = \delta$, the Dirac delta at the origin. For an operator with constant coefficients, convolving $E$ with a source $f$ gives a solution of $P u = f$. Fundamental solutions are the Green's functions of the whole space, and they underlie potential theory, the heat kernel and the theory of wave propagation. See the definition.