Beurling-Landau's density on compact manifolds
Classical Analysis and ODEs
2012-09-28 v1 Spectral Theory
Abstract
Given a compact Riemannian manifold , we consider the subspace of generated by the eigenfunctions of the Laplacian of eigenvalue less than . This space behaves like a space of polynomials and we have an analogy with the Paley-Wiener spaces. We study the interpolating and Marcienkiewicz-Zygmund (M-Z) families and provide necessary conditions for sampling and interpolation in terms of the Beurling-Landau densities. As an application, we prove the equidistribution of the Fekete arrays on some compact manifolds.
Cite
@article{arxiv.1105.2501,
title = {Beurling-Landau's density on compact manifolds},
author = {Joaquim Ortega-Cerdà and Bharti Pridhnani},
journal= {arXiv preprint arXiv:1105.2501},
year = {2012}
}