Shannon sampling and Weak Weyl's Law on compact Riemannian manifolds

2017/03/08 by Isaac Z. Pesenson, Pesenson, Isaac Z.
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1703.03052

openalex publication_date 2017/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The well known Weyl's asymptotic formula gives an approximation to the number N_ω of eigenvalues (counted with multiplicities) on an interval [0,>ω] of the Laplace-Beltrami operator on a compact Riemannian manifold \bf M. In this paper we approach this question from the point of view of Shannon-type sampling on compact Riemannian manifolds. Namely, we give a direct proof that N_ω is comparable to cardinality of certain sampling sets for the subspace of ω-bandlimited functions on \bf M.

Related

• A Weak Weyl's Law on compact metric measure spaces
• Shannon Sampling and Parseval Frames on Compact Manifolds
• A logarithmic improvement in the two-point Weyl law for manifolds without conjugate points
• Almost sure Weyl asymptotics for non-self-adjoint elliptic operators on compact manifolds
• Restriction of Laplace-Beltrami eigenfunctions to arbitrary sets on\n manifolds