{"paper":{"title":"Inverse Bernstein inequalities and min-max-min problems on the unit circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Douglas P. Hardin, Edward B. Saff, Tam\\'as Erd\\'elyi","submitted_at":"2013-07-15T18:56:58Z","abstract_excerpt":"We give a short and elementary proof of an inverse Bernstein-type inequality found by S. Khrushchev for the derivative of a polynomial having all its zeros on the unit circle. The inequality is used to show that equally-spaced points solve a min-max-min problem for the logarithmic potential of such polynomials. Using techniques recently developed for polarization (Chebyshev-type) problems, we show that this optimality also holds for a large class of potentials, including the Riesz potentials $1/r^s$ with $s>0.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4056","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"}