Asymptotics of the d'Alembertian with potential on a pseudo-Riemannian manifold

Let $\square$ be the Laplace-d'Alembert operator on a pseudo-Riemann-
ian manifold $(M,g)$. We derive a series expansion for the fundamental solution $G(x,y)$ of $\square +H$, $H\in C^{\infty }(M)$, which behaves well under various symmetric space dualities. The qualitative properties of this expansion were used in our paper in Invent. Math. 129 (1997), 63-74, to show that the property of vanishing logarithmic term for $G(x,y)$ is preserved under these dualities.