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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Thomas Branson and Gestur Ólafsson
Journal: Proc. Amer. Math. Soc. 127 (1999), 1339-1345
MSC (1991): Primary 47F05
Published electronically: January 28, 1999
MathSciNet review: 1473656
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [BO] T. Branson and G. Ólafsson, Helmholtz operators and symmetric space duality, Invent. Math. 129 (1997), 63-74. CMP 97:16
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Additional Information

Thomas Branson
Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
Email: branson@math.uiowa.edu

Gestur Ólafsson
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: olafsson@marais.math.lsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04621-3
PII: S 0002-9939(99)04621-3
Received by editor(s): July 8, 1997
Received by editor(s) in revised form: August 6, 1997
Published electronically: January 28, 1999
Additional Notes: Research of both authors partially supported by NSF grants.
Research of the second author partially supported by a LEQSF grant.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1999 American Mathematical Society