Boundary behavior of analytic functions on certain Banach spaces

Hector N. Salas

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arXiv · 2510.10373

Boundary behavior of analytic functions on certain Banach spaces

Hector N. Salas

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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.

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Hector N. Salas. 2025-10-12. Boundary behavior of analytic functions on certain Banach spaces. https://arxiv.org/abs/2510.10373

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