{"paper":{"title":"The augmented operator of a surjective partial differential operator with constant coefficients need not be surjective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Thomas Kalmes","submitted_at":"2011-05-24T15:39:53Z","abstract_excerpt":"For $d\\geq 3$ we give an example of a constant coefficient surjective differential operator $P(D):\\mathscr{D}'(X)\\rightarrow\\mathscr{D}'(X)$ over some open subset $X\\subset\\R^d$ such that $P^+(D):\\mathscr{D}'(X\\times\\R)\\rightarrow\\mathscr{D}'(X\\times\\R)$ is not surjective, where $P^+(x_1,...,x_{d+1}):=P(x_1,...,x_d)$. This answers in the negative a problem posed by Bonet and Doma\\'nski in \\cite[Problem 9.1]{Bonet}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4805","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"}