{"paper":{"title":"$L^2$ Serre Duality on Domains in Complex Manifolds and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Debraj Chakrabarti, Mei-Chi Shaw","submitted_at":"2010-06-16T01:03:22Z","abstract_excerpt":"An $L^2$ version of the Serre duality on domains in complex manifolds involving duality of Hilbert space realizations of the $\\bar{\\partial}$-operator is established. This duality is used to study the solution of the $\\bar{\\partial}$-equation with prescribed support. Applications are given to $\\bar{\\partial}$-closed extension of forms, as well to Bochner-Hartogs type extension of CR functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3117","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"}