{"paper":{"title":"A characterization of the Khavinson-Shapiro conjecture via Fischer operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Hermann Render","submitted_at":"2015-11-05T14:10:43Z","abstract_excerpt":"The Khavinson-Shapiro conjecture states that ellipsoids are the only bounded domains in euclidean space satisfying the following property (KS): the solution of the Dirichlet problem for polynomial data is polynomial. In this paper we show that property (KS) for a domain $\\Omega $ is equivalent to the surjectivity of a Fischer operator associated to the domain $\\Omega .$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01894","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"}