{"paper":{"title":"Semiclassical L^p Estimates of Quasimodes on Curved Hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew Hassell, Melissa Tacy","submitted_at":"2010-02-05T05:29:13Z","abstract_excerpt":"Let M be a compact manifold of dimension n, P = P(h) a semiclassical pseudodifferential operator on M, and u = u(h) an L^2 normalised family of functions such that Pu is O(h) in L^2(M) as h goes to 0. Let H be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L^p norms, p > 2, of u restricted to H, under the assumption that the u are semiclassically localised and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch^d(n;k;p) where k=dimH (except for a logarithmic divergence in the case k = "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1119","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"}