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Linear fractional self-maps of the unit ball

Part of: Special classes of linear operators Holomorphic functions of several complex variables

Published online by Cambridge University Press:  15 November 2023

Michael R. Pilla Open the ORCID record for Michael R. Pilla [Opens in a new window]
Michael R. Pilla*
Affiliation:
Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, United States
*
e-mail: michael.pilla@bsu.edu
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Abstract

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.

Keywords

Linear fractional mapsunit ballself-maps

MSC classification

Primary: 32A10: Holomorphic functions
Secondary: 32A40: Boundary behavior of holomorphic functions 47B50: Operators on spaces with an indefinite metric
Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 2 , June 2024 , pp. 458 - 468
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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