{"paper":{"title":"On the stability of the first order linear recurrence in topological vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Dorian Popa, Mohammad Sal Moslehian","submitted_at":"2010-06-10T02:18:49Z","abstract_excerpt":"Suppose that $\\mathcal{X}$ is a sequentially complete Hausdorff locally convex space over a scalar field $\\mathbb{K}$, $V$ is a bounded subset of $\\mathcal{X}$, $(a_n)_{n\\ge 0}$ is a sequence in $\\mathbb{K}\\setminus\\{0\\}$ with the property\\ $\\ds\\liminf_{n\\to\\infty} |a_n|>1$ and $(b_n)_{n\\ge 0}$ is a sequence in $\\mathcal{X}$. We show that for every sequence $(x_n)_{n\\ge 0}$ in $\\mathcal{X}$ satisfying \\begin{eqnarray*} x_{n+1}-a_nx_n-b_n\\in V\\q(n\\geq 0) \\end{eqnarray*} there exists a unique sequence $(y_n)_{n\\ge 0}$ satisfying the recurrence $y_{n+1}=a_ny_n+b_n\\,\\,(n\\geq 0)$ and for every $q$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1940","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"}