{"paper":{"title":"Geometric properties of the nonlinear resolvent of holomorphic generators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Shoikhet, Mark Elin, Toshiyuki Sugawa","submitted_at":"2019-01-08T03:22:56Z","abstract_excerpt":"Let $f$ be the infinitesimal generator of a one-parameter semigroup $\\left\\{ F_{t}\\right\\} _{t\\ge0}$ of holomorphic self-mappings of the open unit disk $\\Delta$. In this paper we study properties of the family $R$ of resolvents $(I+rf)^{-1}:\\Delta\\to\\Delta~ (r\\ge0)$ in the spirit of geometric function theory. We discovered, in particular, that $R$ forms an inverse L\\\"owner chain of hyperbolically convex functions. Moreover, each element of $R$ satisfies the Noshiro-Warschawski condition and is a starlike function of order at least $\\frac12$,. This, in turn, implies that each element of $R$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02142","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"}