Beurling-Landau's density on compact manifolds

Abstract

Given a compact Riemannian manifold $M$, we consider the subspace of $L^2(M)$ generated by the eigenfunctions of the Laplacian of eigenvalue less than $L\ge 1$. 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.

References in corpus (2)

• Carleson Measures and Logvinenko-Sereda sets on compact manifolds
• Equidistribution of Fekete points on complex manifolds

Cited by in corpus (10)

• Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates
• Sampling of real multivariate polynomials and pluripotential theory
• Marcinkiewicz-Zygmund Inequalities for Polynomials in Bergmann and Hardy Spaces
• Uniformly bounded orthonormal polynomials on the sphere
• Kolmogorov and Linear Widths of Balls in Sobolev and Besov Norms on Compact Manifolds
• Discrepancy, separation and Riesz energy of finite point sets on compact connected Riemannian manifolds
• Geometric Space-Frequency Analysis on Manifolds
• Phi-transform on domains
• Necessary Density Conditions for Sampling and Interpolation in Spectral Subspaces of Elliptic Differential Operators
• Sampling, splines and frames on compact manifolds