Boundary behavior of analytic functions on certain Banach spaces

For Banach spaces of analytic functions on the disc for which the polynomials are dense and their pointt evaluations continuous, we prove the following: If they contain a function such that the limit superior of its modulus is infinite almost everywhere on the unit circle, then the same is true for a residual set of functions.

Publication Details

Journal
ArXiv.org
Published
2025-10-12
Primary Topic
Holomorphic and Operator Theory
Type
article
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article

Boundary behavior of analytic functions on certain Banach spaces

ArXiv.org
Holomorphic and Operator Theory
article

Boundary behavior of analytic functions on certain Banach spaces

article en

Abstract

For Banach spaces of analytic functions on the disc for which the polynomials are dense and their pointt evaluations continuous, we prove the following: If they contain a function such that the limit superior of its modulus is infinite almost everywhere on the unit circle, then the same is true for a residual set of functions.

ArXiv.org
Openalex Percentile: Top 35%
Holomorphic and Operator Theory
Open Access PDFOpenAlex
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Boundary behavior of analytic functions on certain Banach spaces · ArXiv.org (2025) | TGRS Research Map | TGRS