{"paper":{"title":"Quasimode, eigenfunction and spectral projection bounds for Schr\\\"odinger operators on manifolds with critically singular potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.SP"],"primary_cat":"math.AP","authors_text":"Christopher D. Sogge, Matthew D. Blair, Yannick Sire","submitted_at":"2019-04-21T21:42:01Z","abstract_excerpt":"We obtain quasimode, eigenfunction and spectral projection bounds for Schr\\\"odinger operators, $H_V=-\\Delta_g+V(x)$, on compact Riemannian manifolds $(M,g)$ of dimension $n\\ge2$, which extend the results of the third author~\\cite{sogge88} corresponding to the case where $V\\equiv 0$. We are able to handle critically singular potentials and consequently assume that $V\\in L^{\\tfrac{n}2}(M)$ and/or $V\\in {\\mathcal K}(M)$ (the Kato class). Our techniques involve combining arguments for proving quasimode/resolvent estimates for the case where $V\\equiv 0$ that go back to the third author \\cite{sogge8"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09665","kind":"arxiv","version":1},"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"}