{"paper":{"title":"On the P\\'olya-Wiman properties of Differential Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Min-Hee Kim, Young-One Kim","submitted_at":"2015-06-01T04:55:10Z","abstract_excerpt":"Let $\\phi(x)=\\sum \\alpha_n x^n$ be a formal power series with real coefficients, and let $D$ denote differentiation. It is shown that \"for every real polynomial $f$ there is a positive integer $m_0$ such that $\\phi(D)^mf$ has only real zeros whenever $m\\geq m_0$\" if and only if \"$\\alpha_0=0$ or $2\\alpha_0\\alpha_2 - \\alpha_1^2 <0$\", and that if $\\phi$ does not represent a Laguerre-P\\'olya function, then there is a Laguerre-P\\'olya function $f$ of genus $0$ such that for every positive integer $m$, $\\phi(D)^mf$ represents a real entire function having infnitely many nonreal zeros."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00350","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"}