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

Let square be the Laplace-d'Alembert operator on a pseudo-Riemannian manifo ld (M; g). We derive a series expansion for the fundamental solution G(x; y ) of square + H, H is an element of C-infinity(M), which behaves well under various symmetric space dualities. The qualitative properties of this expa nsion were used in our paper in Invent. Math. 129 (1997), 63-74, to show th at the property of vanishing logarithmic term for G(x; y) is preserved unde r these dualities.