English

Beurling-Landau's density on compact manifolds

Classical Analysis and ODEs 2012-09-28 v1 Spectral Theory

Abstract

Given a compact Riemannian manifold MM, we consider the subspace of L2(M)L^2(M) generated by the eigenfunctions of the Laplacian of eigenvalue less than L1L\geq 1. 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}
}
R2 v1 2026-06-21T18:06:25.649Z