Shannon Sampling and Weak Weyl’s Law on Compact Riemannian Manifolds

Abstract

The well known Weyl’s asymptotic formula gives an approximation to the number of eigenvalues (counted with multiplicities) on an interval of an elliptic second-order differential self-adjoint non-negative operator on a compact Riemannian manifold 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 is comparable to cardinality of certain sampling sets for the subspace of -bandlimited functions on.