{"paper":{"title":"Krein-like extensions and the lower boundedness problem for elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Gerd Grubb","submitted_at":"2010-02-24T14:20:28Z","abstract_excerpt":"For selfadjoint extensions tilde-A of a symmetric densely defined positive operator A_min, the lower boundedness problem is the question of whether tilde-A is lower bounded {\\it if and only if} an associated operator T in abstract boundary spaces is lower bounded. It holds when the Friedrichs extension A_gamma has compact inverse (Grubb 1974, also Gorbachuk-Mikhailets 1976); this applies to elliptic operators A on bounded domains.\n  For exterior domains, A_gamma ^{-1} is not compact, and whereas the lower bounds satisfy m(T)\\ge m(tilde-A), the implication of lower boundedness from T to tilde-A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4549","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"}