{"paper":{"title":"On the roots of a hyperbolic polynomial pencil","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Victor Katsnelson","submitted_at":"2016-04-27T02:36:15Z","abstract_excerpt":"Let $\\nu_0(t),\\nu_1(t),\\,\\ldots\\,,\\nu_n(t)$ be the roots of the equation $R(z)=t$, where $R(z)$ is a rational function of the form \\[R(z)=z+\\sum\\limits_{k=1}^n\\frac{\\alpha_k}{z-\\mu_k},\\] $\\mu_k$ are pairwise different real numbers, $\\alpha_k>0,\\,1\\leq{}k\\leq{}n$. Then for each real $\\xi$, the function $e^{\\xi\\nu_0(t)}+e^{\\xi\\nu_1(t)}+\\,\\cdots\\,+e^{\\xi\\nu_n(t)}$ is exponentially convex on the interval $-\\infty<t<\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07909","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"}