Beurling–Landauʼs density on compact manifolds

Given a compact Riemannian manifold M, we consider the subspace of L2(M) generated by the eigenfunctions of the Laplacian of eigenvalue less than L⩾1. This space behaves like a space of polynomials and we have an analogy with the Paley–Wiener spaces. We study the interpolating and Marcinkiewicz–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.