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Ferreira, Gustavo R.
(2022).
DOI: https://doi.org/10.1112/blms.12779
Abstract
A well‐known problem in holomorphic dynamics is to obtain Denjoy–Wolff‐type results for compositions of self‐maps of the unit disc. Here, we tackle the particular case of inner functions: if f n : D → D are inner functions fixing the origin, we show that a limit function of f n ∘ ⋯ ∘ f 1
is either constant or an inner function. For the special case of Blaschke products, we prove a similar result and show, furthermore, that imposing certain conditions on the speed of convergence guarantees L 1
convergence of the boundary extensions. We give a counterexample showing that, without these extra conditions, the boundary extensions may diverge at all points of ∂ D
.
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- Item ORO ID
- 86588
- Item Type
- Journal Item
- ISSN
- 1469-2120
- Academic Unit or School
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Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
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