{"paper":{"title":"On the existence of compacta of minimal capacity in the theory of rational approximation of multi-valued analytic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sergey P. Suetin, Viktor I. Buslaev","submitted_at":"2015-05-22T15:19:55Z","abstract_excerpt":"For an interval $E=[a,b]$ on the real line, let $\\mu$ be either the equilibrium measure, or the normalized Lebesgue measure of $E$, and let $V^{\\mu}$ denote the associated logarithmic potential. In the present paper, we construct a function $f$ which is analytic on $E$ and possesses four branch points of second order outside of $E$ such that the family of the admissible compacta of $f$ has no minimizing elements with regard to the extremal theoretic-potential problem, in the external field equals $V^{-\\mu}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06120","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"}