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

 

Quantum unique ergodicity


Author: Harold Donnelly
Journal: Proc. Amer. Math. Soc. 131 (2003), 2945-2951
MSC (2000): Primary 58G25
Published electronically: December 30, 2002
MathSciNet review: 1974353
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Abstract: Consider a compact Riemannian manifold with ergodic geodesic flow. Quantum ergodicity is generalized from orthonormal bases of eigenfunctions of the Laplacian to packets of eigenfunctions. It is shown that this more general result is sharp. Namely, there may exist exceptional packets of eigenfunctions which concentrate on a submanifold.


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Additional Information

Harold Donnelly
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47906

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06810-7
PII: S 0002-9939(02)06810-7
Received by editor(s): March 15, 2002
Received by editor(s) in revised form: April 1, 2002
Published electronically: December 30, 2002
Additional Notes: Research supported by the Ellentuck Fund and the National Science Foundation
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2002 American Mathematical Society