A fundamental solution of a linear differential operator 
is a distribution 
satisfying
 |
where 
is the delta function. If 
has constant coefficients and the operations are defined,
then 
is a solution of 
,
since differentiation commutes with convolution.
A fundamental solution describes the response to a point source. Boundary conditions are not part of its definition. By contrast, a Green's function generally incorporates boundary conditions and may depend on both the source and observation points rather than only on their difference.
