Green's Function

A kernel (distributional or classical) that acts as a right-inverse of a linear differential or integral operator under specified boundary conditions, mapping sources to responses by convolution or integral against the kernel.

A kernel function G(x, s) that represents the response of a linear differential operator L to a point source (delta distribution) located at s, so that L[G(·,s)]=δ(·−s); used to construct particular solutions of linear inhomogeneous boundary-value problems by convolution or integration against source terms.

A kernel function that represents the inverse (or parametrix) of a linear differential operator on a domain with specified boundary conditions; used to construct solutions to linear boundary value problems by superposition of responses to point sources.