{"paper":{"title":"Faber series for $L^2$ holomorphic one-forms on Riemann surfaces with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Eric Schippers, Mohammad Shirazi","submitted_at":"2023-03-28T01:58:33Z","abstract_excerpt":"Consider a compact surface $\\mathscr{R}$ with distinguished points $z_1,\\ldots,z_n$ and conformal maps $f_k$ from the unit disk into non-overlapping quasidisks on $\\mathscr{R}$ taking $0$ to $z_k$. Let $\\Sigma$ be the Riemann surface obtained by removing the closures of the images of $f_k$ from $\\mathscr{R}$.\n  We define forms which are meromorphic on $\\mathscr{R}$ with poles only at $z_1,\\ldots,z_n$, which we call Faber-Tietz forms. These are analogous to Faber polynomials in the sphere. We show that any $L^2$ holomorphic one-form on $\\Sigma$ is uniquely expressible as a series of Faber-Tietz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.15677","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.15677/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}