PreprintCC BY 4.0arXiv
On Simply Connected Domains Supporting an Unbounded Analytic Function with Bounded Derivative
Abstract
In this paper we provide a geometric characterization of simply connected domains in the complex plane supporting an unbounded analytic function with bounded derivative, providing a partial answer to Problem 1.45 in the Hayman List. For a given simply connected domain this characterization is achieved by estimating above and below the norms of certain evaluation functionals on a suitable Banach space of analytic functions on that domain by geometric quantities.
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BibTeX
@misc{macmahon2026simply,
title = {{On Simply Connected Domains Supporting an Unbounded Analytic Function with Bounded Derivative}},
author = {Cameron MacMahon},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20607},
eprint = {2609.20607},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20607},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Simply Connected Domains Supporting an Unbounded Analytic Function with Bounded Derivative
AU - Cameron MacMahon
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20607
UR - https://arxiv.org/abs/2609.20607
AB - In this paper we provide a geometric characterization of simply connected domains in the complex plane supporting an unbounded analytic function with bounded derivative, providing a partial answer to Problem 1.45 in the Hayman List. For a given simply connected domain this characterization is achieved by estimating above and below the norms of certain evaluation functionals on a suitable Banach space of analytic functions on that domain by geometric quantities.
ER -