= Adjoint Green function
An adjoint <Green's function> solves the corresponding adjoint point-source problem, with boundary or terminal conditions chosen so that <integration by parts> gives a representation for a solution of the original operator. For $L=\partial_t-\partial_x^2+c$ on the real line, the formal adjoint is $L^*=-\partial_t-\partial_x^2+c$. The backward kernel with terminal <Dirac delta> at $(\xi,\tau)$ is the translated <heat kernel with constant absorption>, defined for $t<\tau$. Its pairing with a homogeneous forward solution is constant in $t$; taking the terminal limit evaluates that solution at $(\xi,\tau)$.
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