{"paper":{"title":"The sectorial projection defined from logarithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.SP"],"primary_cat":"math.AP","authors_text":"Gerd Grubb","submitted_at":"2011-02-20T07:58:12Z","abstract_excerpt":"For a classical elliptic pseudodifferential operator P of order m>0 on a closed manifold X, such that the eigenvalues of the principal symbol p_m(x,\\xi) have arguments in \\,]\\theta,\\phi [\\, and \\,]\\phi, \\theta +2\\pi [\\, (\\theta <\\phi <\\theta +2\\pi), the sectorial projection \\Pi_{\\theta, \\phi}(P) is defined essentially as the integral of the resolvent along {e^{i\\phi}R_+}\\cup {e^{i\\theta}R_+}. In a recent paper, Booss-Bavnbek, Chen, Lesch and Zhu have pointed out that there is a flaw in several published proofs that \\P_{\\theta, \\phi}(P) is a \\psi do of order 0; namely that p_m(x,\\xi) cannot in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4051","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"}