Geodesic
At the crossroads of holomorphic dynamic and operator theory: spectral properties of composition operators on $\mathrm {Hol}(\mathbb {B}_N)$
Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1289-1314

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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.
DOI : 10.4153/S000843952510074X
Mots-clés : Composition operator, spectrum, holomorphic functions in several variables, Fréchet space 
Oger, Lucas. At the crossroads of holomorphic dynamic and operator theory: spectral properties of composition operators on $\mathrm {Hol}(\mathbb {B}_N)$. Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1289-1314. doi: 10.4153/S000843952510074X
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