Geodesic
Linear fractional self-maps of the unit ball
Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 458-468

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DOI

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.
DOI : 10.4153/S0008439523000887
Mots-clés : Linear fractional maps, unit ball, self-maps 
Pilla, Michael R. Linear fractional self-maps of the unit ball. Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 458-468. doi: 10.4153/S0008439523000887
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     author = {Pilla, Michael R.},
     title = {Linear fractional self-maps of the unit ball},
     journal = {Canadian mathematical bulletin},
     pages = {458--468},
     year = {2024},
     volume = {67},
     number = {2},
     doi = {10.4153/S0008439523000887},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439523000887/}
}
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