### Abstract

By definition a homogeneous Lie group is a Lie group equipped with a family of dilations compatible with the group law. The abelian group (Rn, +) is the very first example of homogeneous Lie group. Homogeneous Lie groups have proved to be a natural setting to generalise many questions of Euclidean harmonic analysis. Indeed, having both the group and dilation structures allows one to introduce many notions coming from the Euclidean harmonic analysis. There are several important differences between the Euclidean setting and the one of homogeneous Lie groups. For instance the operators appearing in the latter setting are usually more singular than their Euclidean counterparts. However it is possible to adapt the technique in harmonic analysis to still treat many questions in this more abstract setting.

Original language | English |
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Title of host publication | Quantization on Nilpotent Lie Groups |

Publisher | Birkhäuser |

Pages | 91-170 |

Number of pages | 80 |

ISBN (Print) | 9783319295572 |

DOIs | |

Publication status | Published - Mar 2016 |

### Publication series

Name | Progress in Mathematics |
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Volume | 314 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Geometry and Topology

### Cite this

*Quantization on Nilpotent Lie Groups*(pp. 91-170). (Progress in Mathematics; Vol. 314). Birkhäuser. https://doi.org/10.1007/978-3-319-29558-9_3

**Homogeneous lie groups.** / Fischer, Veronique; Ruzhansky, Michael.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Quantization on Nilpotent Lie Groups.*Progress in Mathematics, vol. 314, Birkhäuser, pp. 91-170. https://doi.org/10.1007/978-3-319-29558-9_3

}

TY - CHAP

T1 - Homogeneous lie groups

AU - Fischer, Veronique

AU - Ruzhansky, Michael

PY - 2016/3

Y1 - 2016/3

N2 - By definition a homogeneous Lie group is a Lie group equipped with a family of dilations compatible with the group law. The abelian group (Rn, +) is the very first example of homogeneous Lie group. Homogeneous Lie groups have proved to be a natural setting to generalise many questions of Euclidean harmonic analysis. Indeed, having both the group and dilation structures allows one to introduce many notions coming from the Euclidean harmonic analysis. There are several important differences between the Euclidean setting and the one of homogeneous Lie groups. For instance the operators appearing in the latter setting are usually more singular than their Euclidean counterparts. However it is possible to adapt the technique in harmonic analysis to still treat many questions in this more abstract setting.

AB - By definition a homogeneous Lie group is a Lie group equipped with a family of dilations compatible with the group law. The abelian group (Rn, +) is the very first example of homogeneous Lie group. Homogeneous Lie groups have proved to be a natural setting to generalise many questions of Euclidean harmonic analysis. Indeed, having both the group and dilation structures allows one to introduce many notions coming from the Euclidean harmonic analysis. There are several important differences between the Euclidean setting and the one of homogeneous Lie groups. For instance the operators appearing in the latter setting are usually more singular than their Euclidean counterparts. However it is possible to adapt the technique in harmonic analysis to still treat many questions in this more abstract setting.

UR - http://www.scopus.com/inward/record.url?scp=85019654876&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/978-3-319-29558-9_3

U2 - 10.1007/978-3-319-29558-9_3

DO - 10.1007/978-3-319-29558-9_3

M3 - Chapter

SN - 9783319295572

T3 - Progress in Mathematics

SP - 91

EP - 170

BT - Quantization on Nilpotent Lie Groups

PB - Birkhäuser

ER -