Nowhere differentiable functions of analytic type on products of\n finitely connected planar domains

2016/08/29 by Vlassis Mastrantonis, Christoforos Panagiotis, Mastrantonis, Vlassis +1
Mathematics · #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1608.08235

openalex publication_date 2016/08/29 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Using Laurent decomposition and Mergelyan's theorem combined with Baire's\ncategory theorem, we prove generic nowhere differentiability on the\ndistinguished boundary of functions of analytic type on products of planar\ndomains bounded by finitely many disjoint Jordan curves. The parametrization of\nthe boundaries are those induced by the natural Riemann maps.\n

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