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PreprintCC BY-NC-ND 4.0HAL

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

  • Frédéric 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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Cite

BibTeXRIS
BibTeX
@misc{bayart2026semigroup,
  title = {{Semigroup of composition operators on the Fock space of several complex variables}},
  author = {Frédéric Bayart and Maofa Wang and Xingxing Yao},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26349},
  eprint = {2610.26349},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05805315v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Semigroup of composition operators on the Fock space of several complex variables
AU  - Frédéric Bayart
AU  - Maofa Wang
AU  - Xingxing Yao
PY  - 2026
DA  - 2026/10/19
PB  - HAL
DO  - 10.48550/arxiv.2610.26349
UR  - https://hal.science/hal-05805315v1
AB  - 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.
ER  -