## Abstract

We construct coherent states for each eigenspace of a magnetic Lapla-cian on the complex projective n-space in order to apply a quantization-dequantization method. Doing so allows to define the Berezin transform for these spaces. We then establish a formula for this transform as a function of the Fubini–Study Laplacian in a closed form involving of a terminating Kampé de Fériet function. For the lowest spherical Landau level on the Riemann sphere the obtained formula reduces to the one derived by Berezin himself.

Original language | English (US) |
---|---|

Pages (from-to) | 422-440 |

Number of pages | 19 |

Journal | Journal of Mathematical Physics, Analysis, Geometry |

Volume | 17 |

Issue number | 4 |

DOIs | |

State | Published - 2021 |

## Keywords

- Berezin trans-form
- Clebsh–Gordan type relation
- Coherent states
- Complex projective space
- Fubini–Study Laplacian
- Kampé de Fériet function
- Koornwinder’s formula
- Magnetic Laplacians

## ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Geometry and Topology

## Fingerprint

Dive into the research topics of 'Berezin transforms attached to landau levels on the complex projective space p^{n}(c)'. Together they form a unique fingerprint.