{"paper":{"title":"Bergman interpolation on finite Riemann surfaces. Part II: Poincar\\'e-Hyperbolic Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Dror Varolin","submitted_at":"2015-01-09T18:40:24Z","abstract_excerpt":"We formulate the Bergman-type interpolation problem on finite open Riemann surfaces covered by the unit disk. Our version of the interpolation problem generalizes Bergman-type interpolation problems previously studied by Seip, Berntsson, Ortega Cerd\\`a, and a number of other authors. We then prove necessary and sufficient conditions for interpolation, and also some sufficient conditions under even weaker hypotheses. The results extend work of Ortega Cerd\\`a, who resolved the case in which the boundary of the surface is pure $1$-dimensional. Our version of the interpolation problem effectively "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02225","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"}