{"paper":{"title":"Images of nowhere differentiable Lipschitz maps of $[0,1]$ into $L_1[0,1]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Florin Catrina, Mikhail I. Ostrovskii","submitted_at":"2017-05-24T18:17:39Z","abstract_excerpt":"The main result: for every sequence $\\{\\omega_m\\}_{m=1}^\\infty$ of positive numbers ($\\omega_m>0)$ there exists an isometric embedding $F:[0,1]\\to L_1[0,1]$ which is nowhere differentiable, but for each $t\\in [0,1]$ the image $F_t$ is infinitely differentiable on $[0,1]$ with bounds $\\max_{x\\in[0,1]}|F_t^{(m)}(x)|\\le\\omega_m$ and has an analytic extension to the complex plane which is an entire function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08916","kind":"arxiv","version":2},"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"}