{"paper":{"title":"Koppelman formulas and the $\\dbar$-equation on an analytic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"H{\\aa}kan Samuelsson, Mats Andersson","submitted_at":"2008-01-04T17:19:07Z","abstract_excerpt":"Let $X$ be an analytic space of pure dimension. We introduce a formalism to generate intrinsic weighted Koppelman formulas on $X$ that provide solutions to the $\\dbar$-equation. We prove that if $\\phi$ is a smooth $(0,q+1)$-form on a Stein space $X$ with $\\dbar\\phi=0$, then there is a smooth $(0,q)$-form $\\psi$ on $X_{reg}$ with at most polynomial growth at $X_{sing}$ such that $\\dbar\\psi=\\phi$. The integral formulas also give other new existence results for the $\\dbar$-equation and Hartogs theorems, as well as new proofs of various known results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.0710","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"}