SHANNON-TYPE SAMPLING AND WEYL’S LAW ON RIEMANNIAN MANIFOLDS
The well known Weyl’s asymptotic formula gives an approxima-
tion to the number Nω of eigenvalues (counted with multiplicities) on an inter-
val [0, ω] of the Laplace-Beltrami operator on a compact Riemannian manifold
M. In this paper we approach this question from the point of view of Shannon-
type sampling on compact Riemannian manifolds. Namely, we show directly
that Nω is comparable to cardinality of certain sampling sets for the subspace
of ω-bandlimited functions on M.