Quantum unique ergodicity

Author:
Harold Donnelly

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2945-2951

MSC (2000):
Primary 58G25

DOI:
https://doi.org/10.1090/S0002-9939-02-06810-7

Published electronically:
December 30, 2002

MathSciNet review:
1974353

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-02-06810-7

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