{"paper":{"title":"On the Interpolation of Analytic Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A.A. Shkalikov, A.M. Savchuk","submitted_at":"2013-07-02T08:33:43Z","abstract_excerpt":"Let (E_0,E_1) and (H_0,H_1) be a pair of Banach spaces with dense and continuous embeddings E_1 into E_0, H_1 into H_0. For $\\theta \\in [0,1]$ denote by $B_\\theta(0,R)$ the ball of radius R centered at zero in the interpolation spaces E_\\theta. Assume that an analytic map $\\Phi$ maps the ball B_0(0,R) into H_0, $\\Phi$ maps B_1(0,R) into H_1 and for $\\theta =0,1$ the estimates $$ \\|\\Phi(x)\\|_{H_\\theta} \\le C_\\theta\\|x\\|_{H_\\theta}, \\forall\\ x\\in B_\\theta(0,R), $$ hold. Then for all $\\theta\\in(0, 1)$ and r<R $\\Phi$ maps the ball $B_\\theta (0,r)$ into $H_\\theta$ and the same estimate holds for $x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0623","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"}