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

Branson, Thomas; Ólafsson, Gestur

doi:10.1090/S0002-9939-99-04621-3

Asymptotics of the d’Alembertian with potential on a pseudo-Riemannian manifold
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by Thomas Branson and Gestur Ólafsson PDF

Proc. Amer. Math. Soc. 127 (1999), 1339-1345 Request permission

Abstract:

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.

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