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Concentration of Symmetric Eigenfunction

Azagra Rueda, Daniel and Macia Lang , Fabricio (2010) Concentration of Symmetric Eigenfunction. Nonlinear Analysis: Theory, Methods & Applications , 73 (3). pp. 683-688. ISSN 0362-546X

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Abstract

In this article we examine the concentration and oscillation effects developed by high-frequency eigenfunctions of the Laplace operator in a compact Riemannian manifold. More precisely, we are interested in the structure of the possible invariant semiclassical measures obtained as limits of Wigner measures corresponding to eigenfunctions. These measures describe simultaneously the concentration and oscillation effects developed by a sequence of eigenfunctions. We present some results showing how to obtain invariant semiclassical measures from eigenfunctions with prescribed symmetries. As an application of these results, we give a simple proof of the fact that in a manifold of constant positive sectional curvature, every measure which is invariant by the geodesic flow is an invariant semiclassical measure.

Item Type:Article
Uncontrolled Keywords:Eigenfunctions of the Laplacian; Semiclassical measures; Wigner distributions; Manifolds of constant sectional curvature; Invariant measures
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:12910
Deposited On:12 Jul 2011 07:15
Last Modified:06 Feb 2014 09:36

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