### Abstract

This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups.

The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.

The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.

Original language | English |
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Publisher | Birkhäuser |

Number of pages | 557 |

Volume | 314 |

Edition | Progress in Mathematics |

ISBN (Electronic) | 978-3-319-29558-9 |

ISBN (Print) | 978-3-319-29557-2 |

Publication status | Published - Apr 2016 |

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## Profiles

### Veronique Fischer

- Department of Mathematical Sciences - Senior Lecturer
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)

Person: Research & Teaching

## Cite this

Fischer, V., & Michael, R. (2016).

*Quantization on nilpotent Lie group*. (Progress in Mathematics ed.) Birkhäuser.