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A critical majorant for the Khinchin-Ostrowski property
Bartosz Malman
https://arxiv.org/abs/2506.06911 https://arxiv.org/pdf/2506.06…

A critical majorant for the Khinchin-Ostrowski property
In this short note we prove an optimal version of a classical result. Given a majorant determining a growth restriction on functions in the unit disk $\mathbb{D}$, we say that a set $E$ on the unit circle $\mathbb{T}$ is a uniqueness set, or has the Khinchin-Ostrowski property, with respect to the majorant, if any sequence of analytic polynomials satisfying the growth restriction which converges in an appropriate sense to $0$ on $E$, in fact is forced to converge to $0$ in $\mathbb{D}$ also. Th…