{"paper":{"title":"Resolvent at low energy III: the spectral measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Adam Sikora, Andrew Hassell, Colin Guillarmou","submitted_at":"2010-09-16T03:24:27Z","abstract_excerpt":"Let $M^\\circ$ be a complete noncompact manifold and $g$ an asymptotically conic Riemaniann metric on $M^\\circ$, in the sense that $M^\\circ$ compactifies to a manifold with boundary $M$ in such a way that $g$ becomes a scattering metric on $M$. Let $\\Delta$ be the positive Laplacian associated to $g$, and $P = \\Delta + V$, where $V$ is a potential function obeying certain conditions. We analyze the asymptotics of the spectral measure $dE(\\lambda) = (\\lambda/\\pi i) \\big(R(\\lambda+i0) - R(\\lambda - i0) \\big)$ of $P_+^{1/2}$, where $R(\\lambda) = (P - \\lambda^2)^{-1}$, as $\\lambda \\to 0$, in a mann"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3084","kind":"arxiv","version":2},"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"}