SHANNON-TYPE SAMPLING AND WEYL’S LAW ON RIEMANNIAN MANIFOLDS

Mon, 18/09/2017 - 14:00
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Abstract: 

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.