{"paper":{"title":"Generators for rings of compactly supported distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.RA"],"primary_cat":"math.FA","authors_text":"Amol Sasane, Sara Maad Sasane","submitted_at":"2010-04-06T18:53:53Z","abstract_excerpt":"Let $C$ denote a closed convex cone $C$ in $\\mathbb{R}^d$ with apex at 0. We denote by $\\mathcal{E}'(C)$ the set of distributions having compact support which is contained in $C$. Then $\\mathcal{E}'(C)$ is a ring with the usual addition and with convolution. We give a necessary and sufficient analytic condition on $\\hat{f}_1,..., \\hat{f}_n$ for $f_1,...,f_n \\in \\mathcal{E}'(C)$ to generate the ring $\\mathcal{E}'(C)$.  (Here $\\hat{\\cdot}$ denotes Fourier-Laplace transformation.) This result is an application of a general result on rings of analytic functions of several variables by H\\\"ormander."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0927","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"}