{"paper":{"title":"A model space approach to some classical inequalities for rational functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anton Baranov, Rachid Zarouf (LATP)","submitted_at":"2013-10-04T06:38:35Z","abstract_excerpt":"We consider the set \\mathcal{R}_{n} of rational functions of degree at most n\\geq1 with no poles on the unit circle \\mathbb{T} and its subclass \\mathcal{R}_{n,\\, r} consisting of rational functions without poles in the annulus \\left\\{\\xi:\\; r\\leq|\\xi|\\leq\\frac{1}{r}\\right\\}. We discuss an approach based on the model space theory which brings some integral representations for functions in \\mathcal{R}_{n} and their derivatives. Using this approach we obtain L^{p}-analogs of several classical inequalities for rational functions including the inequalities by P. Borwein and T. Erd\\'elyi, the Spijke"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1182","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"}