{"paper":{"title":"Derivatives of rational inner functions: geometry of singularities and integrability at the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.FA"],"primary_cat":"math.CV","authors_text":"Alan Sola, James Eldred Pascoe, Kelly Bickel","submitted_at":"2017-03-12T23:33:32Z","abstract_excerpt":"We analyze the singularities of rational inner functions on the unit bidisk and study both when these functions belong to Dirichlet-type spaces and when their partial derivatives belong to Hardy spaces. We characterize derivative $H^{\\mathfrak{p}}$ membership purely in terms of contact order, a measure of the rate at which the zero set of a rational inner function approaches the distinguished boundary of the bidisk. We also show that derivatives of rational inner functions with singularities fail to be in $H^{\\mathfrak{p}}$ for $\\mathfrak{p}\\ge\\frac{3}{2}$ and that higher non-tangential regula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04198","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"}