{"paper":{"title":"On harmonic convolutions involving a vertical strip mapping","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":"2013-07-24T03:55:46Z","abstract_excerpt":"Let f_\\beta = h_\\beta+\\bar{g}_\\beta and F_a = H_a +\\bar{G}_a be harmonic mappings obtained by shearing of analytic mappings h_\\beta +g_\\beta = 1/(2i\\sin\\beta)log((1 + ze^{i\\beta})/(1 + ze^{-i\\beta})), 0<\\beta<\\pi and H_a+G_a = z/(1-z), respectively. Kumar et al. [5] conjectured that if \\omega(z)=e^{i\\theta}z^n (\\theta\\in R, n\\in N) and \\omega_a(z)=(a-z)/(1-az), a\\in(-1,1) are dilatations of f_\\beta and F_a, respectively, then F_a\\ast f_\\beta \\in S_H^0 and is convex in the direction of the real axis provided a\\in[(n-2)/(n + 2), 1).They claimed to have verified the result for n = 1, 2, 3 and 4 o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6292","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"}