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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Quantum unique ergodicity
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by Harold Donnelly PDF
Proc. Amer. Math. Soc. 131 (2003), 2945-2951 Request permission

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
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 2945-2951
  • MSC (2000): Primary 58G25
  • DOI: https://doi.org/10.1090/S0002-9939-02-06810-7
  • MathSciNet review: 1974353