{"paper":{"title":"Topological genericity of nowhere differentiable functions in the disc algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Alexandros Eskenazis","submitted_at":"2013-11-01T11:16:10Z","abstract_excerpt":"In this paper we introduce a class of functions contained in the disc algebra $\\mathcal{A}(D)$. We study functions $f \\in \\mathcal{A}(D)$, which have the property that the continuous periodic function $u = Ref|_{\\mathbb{T}}$, where $\\mathbb{T}$ is the unit circle, is nowhere differentiable. We prove that this class is non-empty and instead, generically, every function $f \\in \\mathcal{A}(D)$ has the above property. Afterwards, we strengthen this result by proving that, generically, for every function $f \\in \\mathcal{A}(D)$, both continuous periodic functions $u=Ref|_\\mathbb{T}$ and $\\tilde{u} ="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0142","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"}