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arXiv · 2610.26349

Semigroup of composition operators on the Fock space of several complex variables

Fr{é}d{é}ric Bayart·Maofa Wang·Xingxing Yao
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Abstract

This paper considers discrete and continuous semigroups of composition operators on the Fock space of several complex variables. For discrete semigroups generated by a single operator, the asymptotic behaviour is analysed. Strongly continuous semigroups are studied, and in particular it is shown that the classical Berkson-Porta theorem fails in this context. As an application, we show that any bounded composition operator is strongly reducible on the Fock space and that it is mean-ergodic.

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Fr{é}d{é}ric Bayart, Maofa Wang, Xingxing Yao. 2026-10-19. Semigroup of composition operators on the Fock space of several complex variables. https://arxiv.org/abs/2610.26349

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