{"paper":{"title":"Interpolation of nonlinear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Savchuk, A. Shkalikov, P. Topalov, T. Kappeler","submitted_at":"2014-05-16T17:47:20Z","abstract_excerpt":"Let $(X_0, X_1)$ and $(Y_0, Y_1)$ be complex Banach couples and assume that $X_1\\subseteq X_0$ with norms satisfying $\\|x\\|_{X_0} \\le c\\|x\\|_{X_1}$ for some $c > 0$. For any $0<\\theta <1$, denote by $X_\\theta = [X_0, X_1]_\\theta$ and $Y_\\theta = [Y_0, Y_1]_\\theta$ the complex interpolation spaces and by $B(r, X_\\theta)$, $0 \\le \\theta \\le 1,$ the open ball of radius $r>0$ in $X_\\theta$, centered at zero. Then for any analytic map $\\Phi: B(r, X_0) \\to Y_0+ Y_1$ such that $\\Phi: B(r, X_0)\\to Y_0$ and $\\Phi: B(c^{-1}r, X_1)\\to Y_1$ are continuous and bounded by constants $M_0$ and $M_1$, respecti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4253","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"}