Abstract
In this chapter we briefly review the global quantization of operators and symbols on compact Lie groups following [RT13] and [RT10a] as well as more recent developments of this subject in this direction. Especially the monograph [RT10a] can serve as a companion for the material presented here, so we limit ourselves to explaining the main ideas only. This quantization yields full (finite dimensional) matrix-valued symbols for operators due to the fact that the unitary irreducible representations of compact Lie groups are all finite dimensional. Here, in order to motivate the developments on nilpotent groups, which is the main subject of the present monograph, we briefly review key elements of this theory referring to [RT10a] or to other sources for proofs and further details.
Chapter PDF
Keywords
- Linear Continuous Operator
- Fourier Multiplier
- Unitary Irreducible Representation
- Multiplier Theorem
- Symbolic Calculus
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Author information
Authors and Affiliations
Rights and permissions
Open Access. This chapter is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, duplication, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, a link is provided to the Creative Commons license and any changes made are indicated.
The images or other third party material in this chapter are included in the work’s Creative Commons license, unless indicated otherwise in the credit line; if such material is not included in the work’s Creative Commons license and the respective action is not permitted by statutory regulation, users will need to obtain permission from the license holder to duplicate, adapt or reproduce the material.
Copyright information
© 2016 The Author(s)
About this chapter
Cite this chapter
Fischer, V., Ruzhansky, M. (2016). Quantization on compact Lie groups. In: Quantization on Nilpotent Lie Groups. Progress in Mathematics, vol 314. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-29558-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-29558-9_2
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-29557-2
Online ISBN: 978-3-319-29558-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)