{"paper":{"title":"Injectivity of sections of convex harmonic mappings and convolution theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Liulan Li, Saminathan Ponnusamy","submitted_at":"2015-06-01T15:38:25Z","abstract_excerpt":"In the article the authors consider the class ${\\mathcal H}_0$ of sense-preserving harmonic functions $f=h+\\overline{g}$ defined in the unit disk $|z|<1$ and normalized so that $h(0)=0=h'(0)-1$ and $g(0)=0=g'(0)$, where $h$ and $g$ are analytic in the unit disk. In the first part of the article we present two classes $\\mathcal{P}_H^0(\\alpha)$ and $\\mathcal{G}_H^0(\\beta)$ of functions from ${\\mathcal H}_0$ and show that if $f\\in \\mathcal{P}_H^0(\\alpha)$ and $F\\in\\mathcal{G}_H^0(\\beta)$, then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00542","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"}