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Quantization on compact Lie groups

  • Veronique Fischer
  • Michael Ruzhansky
Open Access
Chapter
Part of the Progress in Mathematics book series (PM, volume 314)

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.

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.

Copyright information

© The Author(s) 2016

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.

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Authors and Affiliations

  • Veronique Fischer
    • 1
  • Michael Ruzhansky
    • 2
  1. 1.Department of MathematicsUniversity of BathBathUK
  2. 2.Department of MathematicsImperial College LondonLondonUK

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