Uniform distribution of eigenfunctions on compact hyperbolic surfaces
type: Item
instance of: scholarly article
title: Uniform distribution of eigenfunctions on compact hyperbolic surfaces
zbMATH Open document ID: 0643.58029
DOI: 10.1215/S0012-7094-87-05546-3
author: Steve Zelditch
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: Let X be a compact Riemann surface with a metric of constant curvature - 1. Suppose that \(\phi_ k\) are the eigenfunctions of the Laplace operator of X. The author proves that almost all of these eigenfunctions become uniformly distributed over X, as \(k\to \infty\). In fact, after passing to a subsequence of density one, we have \(\int_{E}\phi\) \(2_ k\to vol(E)/vol(X)\). This result is developed in a more general framework, using a suitable calculus of pseudodifferential operators.
reviewed by: Harold Donnelly
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4048716
zbMATH Keywords: spectrum
zbMATH Keywords: closed geodesics
zbMATH Keywords: eigenfunctions
zbMATH Keywords: Laplace operator
zbMATH Keywords: pseudodifferential operators
MaRDI profile type: Publication
Wikidata QID: Q97994933
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description: scientific article; zbMATH DE number 4048716