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- W4313447654 abstract "Let $mathscr J$ be the space of inner functions of finite entropy endowed with the topology of stable convergence. We prove that an inner function $F in mathscr J$ possesses a radial limit (and in fact, a thick limit) in the unit disk at $sigma(F')$ a.e. point on the unit circle. We use this to show that the singular value measure $nu(F) = sum_{c in text{crit } F} (1-|c|) cdot delta_{F(c)} + F_*(sigma(F'))$ varies continuously in $F$. Our analysis involves a surprising connection between Beurling-Carleson sets and angular derivatives." @default.
- W4313447654 created "2023-01-06" @default.
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- W4313447654 date "2022-12-30" @default.
- W4313447654 modified "2023-10-18" @default.
- W4313447654 title "Critical values of inner functions" @default.
- W4313447654 doi "https://doi.org/10.48550/arxiv.2212.14818" @default.
- W4313447654 hasPublicationYear "2022" @default.
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