{"paper":{"title":"New Topological C-Algebras with Applications in Linear Systems Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Alpay, Guy Salomon","submitted_at":"2011-06-28T18:03:47Z","abstract_excerpt":"Motivated by the Schwartz space of tempered distributions $\\mathscr S^\\prime$ and the Kondratiev space of stochastic distributions $\\mathcal S_{-1}$ we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert spaces $\\mathscr H_p^\\prime,p\\in\\mathbb N$, with decreasing norms $|\\cdot|_{p}$. The elements of these spaces are functions on a free commutative monoid. We characterize those rings in this family which satisfy an inequality of the form $|f * g|_{p} \\leq A(p-q) |f|_{q}|g|_{p}$ for all $p\\ge q+d$, where * denotes the convolution in the monoid, $A(p-q)$ is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5746","kind":"arxiv","version":2},"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"}