### A convergence theorem for harmonic measures with applications to Taylor series

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 Title: A convergence theorem for harmonic measures with applications to Taylor series Authors: Gardiner, Stephen J.Manolaki, Myrto Permanent link: http://hdl.handle.net/10197/7393 Date: Mar-2016 Abstract: Let $f$ be a holomorphic function on the unit disc, and let $(S_{n_{k}})$ be a subsequence of its Taylor polynomials about 0. It is shown that the nontangential limit of $f$ and lim $_{k\rightarrow \infty }S_{n_{k}}$ agree at almost all points of the unit circle where they simultaneously exist. This result yields new information about the boundary behaviour of universal Taylor series. The key to its proof lies in a convergence theorem for harmonic measures that is of independent interest. Type of material: Journal Article Publisher: American Mathematical Society Copyright (published version): 2015 American Mathematical Society Keywords: Boundary behavior of power series; Over-convergence; Capacity and harmonic measure in the complex plane; Universal Taylor series; Potentials and capacity; Harmonic measure; Extremal length; Boundary value and inverse problems DOI: 10.1090/proc/12764 Language: en Status of Item: Peer reviewed Appears in Collections: Mathematics and Statistics Research Collection

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