Uniform distribution of eigenfunctions on compact hyperbolic surfaces
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.
scientific article; zbMATH DE number 4048716
scientific article