{"paper":{"title":"Shannon sampling and Weak Weyl's Law on compact Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Isaac Z. Pesenson","submitted_at":"2017-03-08T22:02:12Z","abstract_excerpt":"The well known Weyl's asymptotic formula gives an approximation to the number $\\mathcal{N}_{\\omega}$ of eigenvalues (counted with multiplicities) on an interval $[0,\\>\\omega]$ 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 $\\mathcal{N}_{\\omega}$ is comparable to cardinality of certain sampling sets for the subspace of $\\omega$-bandlimited functions on ${\\bf M}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03052","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}