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We study circle restrictions of inner functions in the unit disc, showing independent local invertibility, indicating broader characteristics of these functions.
We study the circle restrictions of inner functions on the unit disc showing that the local invertibility of a restriction is independent of its singularity set and proving a local characterization of analytic conditional expectations. We establish central limit properties for some stochastic processes driven by probability preserving restrictions via spectral analysis of their perturbed transfer operators.
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Aaronson et al. (2026) studied this question.
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