{"paper":{"title":"An application of Cohn's rule to convolutions of univalent harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Michael Dorff, Raj Kumar, Sukhjit Singh, Sushma Gupta","submitted_at":"2013-06-23T06:05:10Z","abstract_excerpt":"Dorff et al. [4], proved that the harmonic convolution of right half-plane mapping with dilatation -z and mapping f_\\beta = h_\\beta + \\bar{g}_\\beta, where f_\\beta is obtained by shearing of analytic vertical strip mapping, with dilatation e^{i\\theta}z^n; n = 1,2,\\theta \\in R, is in S_H^0 and is convex in the direction of the real axis. In this paper, by using Cohn's rule, we generalize this result by considering dilatations (a-z)/(1-az), a\\in (-1,1) and e^{i\\theta} z^n (n\\in N;\\theta\\in R) of right half-plane mapping and f_\\beta, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5375","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"}