Homogeneous lie groups

Veronique Fischer, Michael Ruzhansky

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish
Title of host publicationQuantization on Nilpotent Lie Groups
PublisherBirkhäuser
Pages91-170
Number of pages80
ISBN (Print)9783319295572
DOIs
Publication statusPublished - Mar 2016

Publication series

NameProgress in Mathematics
Volume314

Fingerprint

Homogeneous Groups
Euclidean
Harmonic Analysis
Dilation
One to many
Abelian group
Generalise
Operator

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Fischer, V., & Ruzhansky, M. (2016). Homogeneous lie groups. In 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.

Quantization on Nilpotent Lie Groups. Birkhäuser, 2016. p. 91-170 (Progress in Mathematics; Vol. 314).

Research output: Chapter in Book/Report/Conference proceedingChapter

Fischer, V & Ruzhansky, M 2016, Homogeneous lie groups. in 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
Fischer V, Ruzhansky M. Homogeneous lie groups. In Quantization on Nilpotent Lie Groups. Birkhäuser. 2016. p. 91-170. (Progress in Mathematics). https://doi.org/10.1007/978-3-319-29558-9_3
Fischer, Veronique ; Ruzhansky, Michael. / Homogeneous lie groups. Quantization on Nilpotent Lie Groups. Birkhäuser, 2016. pp. 91-170 (Progress in Mathematics).
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