{"paper":{"title":"Plemelj-Sokhotski isomorphism for quasicircles in Riemann surfaces and the Schiffer operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Eric Schippers, Wolfgang Staubach","submitted_at":"2018-11-26T22:13:09Z","abstract_excerpt":"Let $R$ be a compact Riemann surface and $\\Gamma$ be a Jordan curve separating $R$ into connected components $\\Sigma_1$ and $\\Sigma_2$. We consider Calder\\'on-Zygmund type operators $T(\\Sigma_1,\\Sigma_k)$ taking the space of $L^2$ anti-holomorphic one-forms on $\\Sigma_1$ to the space of $L^2$ holomorphic one-forms on $\\Sigma_k$, which we call the Schiffer operators. We extend results of Menahem M. Schiffer and others, which where confined to analytic Jordan curves $\\Gamma$, to general quasicircles in a characterizing manner, and prove new identities for adjoints of the Schiffer operators. Furt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10715","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"}