Stable convergence of inner functions

@article{Ivrii2020StableCO,
  title={Stable convergence of inner functions},
  author={O. V. Ivrii},
  journal={Journal of the London Mathematical Society},
  year={2020},
  volume={102}
}
  • O. Ivrii
  • Published 15 February 2018
  • Mathematics
  • Journal of the London Mathematical Society
Let J be the set of inner functions whose derivative lies in the Nevanlinna class. In this paper, we discuss a natural topology on J where Fn→F if the critical structures of Fn converge to the critical structure of F . We show that this occurs precisely when the critical structures of the Fn are uniformly concentrated on Korenblum stars. The proof uses Liouville's correspondence between holomorphic self‐maps of the unit disk and solutions of the Gauss curvature equation. Building on the works… 
A characterization of one‐component inner functions
We present a characterization of one‐component inner functions in terms of the location of their zeros and their associated singular measure. As consequence we answer several questions posed by Cima

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