A property of boundary extensions of atomic singular inner functions
Iason Efraimidis, Adrian Llinares, Sullivan MacDonald, Ignacio Uriarte-Tuero, Dragan Vukotic
Abstract
Using a property of the Hilbert transform, we prove a measure theoretic result concerning the extensions of atomic singular inner functions to the circle. Various alternative proofs are presented using the mean value theorem for harmonic functions and a well-known property of Blaschke products. Using the main result, we establish several facts concerning atomic singular inner functions and their logarithms.
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