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

 

Exceptional sequences of eigenfunctions for hyperbolic manifolds


Author: Harold Donnelly
Journal: Proc. Amer. Math. Soc. 135 (2007), 1551-1555
MSC (2000): Primary 58J50, 58J53
Published electronically: November 13, 2006
MathSciNet review: 2276666
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Abstract: Examples are given of hyperbolic manifolds in every dimension at least five which support sequences of eigenfunctions for the Laplacian whose $ L^{\infty}$-norms grow as a power of the eigenvalue while their $ L^2$-norms are one.


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Additional Information

Harold Donnelly
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: hgd@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08613-8
PII: S 0002-9939(06)08613-8
Received by editor(s): October 18, 2004
Received by editor(s) in revised form: December 9, 2005
Published electronically: November 13, 2006
Additional Notes: The author was partially supported by NSF Grant 0203070-DMS
Communicated by: Mikhail Shubin
Article copyright: © Copyright 2006 American Mathematical Society