{"paper":{"title":"Resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds II: spectral measure, restriction theorem, spectral multiplier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew Hassell, Xi Chen","submitted_at":"2014-12-14T23:53:32Z","abstract_excerpt":"We consider the Laplacian $\\Delta$ on an asymptotically hyperbolic manifold $X$, as defined by Mazzeo and Melrose. We give pointwise bounds on the spectral measure for the operator $(\\Delta - n^2/4)_+^{1/2}$ on such manifolds, under the assumptions that $X$ is nontrapping and there is no resonance at the bottom of the spectrum. This uses the construction of the resolvent given by Mazzeo and Melrose (valid when the spectral parameter lies in a compact set), Melrose, S\\'a Barreto and Vasy (high energy estimates for a perturbation of the hyperbolic metric) and the present authors (see also the wo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4427","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"}