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.