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At the crossroads of holomorphic dynamic and operator theory: spectral properties of composition operators on $\mathrm {Hol}(\mathbb {B}_N)$

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

Published online by Cambridge University Press:  11 June 2025

Lucas Oger
Lucas Oger*
Affiliation:
https://ror.org/03x42jk29Université Gustave Eiffel, LAMA, (UMR 8050), UPEM, UPEC, CNRS, F-77454, Marne-la-Vallée, France
*
e-mail: lucas.oger@univ-eiffel.fr
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Abstract

We study the class of composition operators acting on the Fréchet space $\mathrm {Hol}(\mathbb {B}_N)$ of all holomorphic maps on the unit ball of $\mathbb {C}^N$. We describe the conditions to make these operators continuous, invertible and compact. We also do the spectral study of these operators, depending on the nature of its symbol.

Keywords

Composition operatorspectrumholomorphic functions in several variablesFréchet space

MSC classification

Primary: 47B33: Composition operators 32A10: Holomorphic functions 47A10: Spectrum, resolvent

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Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 26
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This research is partly supported by the Bézout Labex, funded by ANR, reference ANR-10-LABX-58.

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