{"paper":{"title":"Inversion formulas for complex Radon transform on projective varieties and boundary value problems for systems of linear PDE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Gennadi M. Henkin, Peter L. Polyakov","submitted_at":"2011-06-14T19:34:12Z","abstract_excerpt":"Let $G\\subset \\C P^n$ be a linearly convex compact with smooth boundary, $D={\\C}P^n\\setminus G$, and let $D^* \\subset (\\C P^n)^*$ be the dual domain. Then for an algebraic, not necessarily reduced, complete intersection subvariety $V$ of dimension $d$ we construct an explicit inversion formula for the complex Radon transform $R_V:\\ H^{d,d-1}(V\\cap D)\\to H^{1,0}(D^*)$, and explicit formulas for solutions of an appropriate boundary value problem for the corresponding system of differential equations with constant coefficients on $D^*$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2795","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"}