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Linear fractional self-maps of the unit ball
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 67 / Issue 2 / June 2024
- Published online by Cambridge University Press:
- 15 November 2023, pp. 458-468
- Print publication:
- June 2024
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- Article
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Determining the range of complex maps plays a fundamental role in the study of several complex variables and operator theory. In particular, one is often interested in determining when a given holomorphic function is a self-map of the unit ball. In this paper, we discuss a class of maps in
$\mathbb {C}^N$ that generalize linear fractional maps. We then proceed to determine precisely when such a map is a self-map of the unit ball. In particular, we take a novel approach, obtaining numerous new results about this class of maps along the way.
