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arXiv · 2611.06877

A property of boundary extensions of atomic singular inner functions

Iason Efraimidis·Adrian Llinares·Sullivan MacDonald·Ignacio Uriarte-Tuero·Dragan Vukotic
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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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Iason Efraimidis, Adrian Llinares, Sullivan MacDonald, Ignacio Uriarte-Tuero, Dragan Vukotic. 2026-11-04. A property of boundary extensions of atomic singular inner functions. https://arxiv.org/abs/2611.06877

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