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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Spectral cluster estimates for metrics of Sobolev regularity


Author: Matthew D. Blair
Journal: Trans. Amer. Math. Soc. 361 (2009), 1209-1240
MSC (2000): Primary 42C15; Secondary 35P99, 35L15, 35R05
Published electronically: October 23, 2008
MathSciNet review: 2457396
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Abstract: We investigate spectral cluster estimates for compact manifolds equipped with a Riemannian metric whose regularity is determined by its inclusion in a Sobolev space of sufficiently high order. The problem is reduced to obtaining $ L^p$ estimates for the wave equation which are shown by employing wave packet techniques.


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Additional Information

Matthew D. Blair
Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
Address at time of publication: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131
Email: blair@math.rochester.edu, blair@math.unm.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04638-2
PII: S 0002-9947(08)04638-2
Received by editor(s): August 28, 2006
Published electronically: October 23, 2008
Additional Notes: The author was supported in part by the NSF grant DMS-0354668.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.