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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{efraimidis2026property,
  title = {{A property of boundary extensions of atomic singular inner functions}},
  author = {Iason Efraimidis and Adrian Llinares and Sullivan MacDonald and Ignacio Uriarte-Tuero and Dragan Vukotic},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06877},
  eprint = {2611.06877},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06877},
}
RIS
TY  - UNPB
TI  - A property of boundary extensions of atomic singular inner functions
AU  - Iason Efraimidis
AU  - Adrian Llinares
AU  - Sullivan MacDonald
AU  - Ignacio Uriarte-Tuero
AU  - Dragan Vukotic
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06877
UR  - https://arxiv.org/abs/2611.06877
AB  - 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.
ER  -