{"paper":{"title":"Subspaces of $C^\\infty$ invariant under the differentiation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alexandru Aleman, Anton Baranov, Yurii Belov","submitted_at":"2013-09-26T17:01:48Z","abstract_excerpt":"Let $L$ be a proper differentiation invariant subspace of $C^\\infty(a,b)$ such that the restriction operator $\\frac{d}{dx}\\bigl{|}_L$ has a discrete spectrum $\\Lambda$ (counting with multiplicities). We prove that $L$ is spanned by functions vanishing outside some closed interval $I\\subset(a,b)$ and monomial exponentials $x^ke^{\\lambda x}$ corresponding to $\\Lambda$ if its density does not exceed the critical value $\\frac{|I|}{2\\pi}$, and moreover, we show that the result is not necessarily true when the density of $\\Lambda$ equals the critical value. This answers a question posed by the first"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6968","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"}