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Quantization on Nilpotent Lie Groups

Part of the Progress in Mathematics Book Series (volume 314)

DOI: 10.1007/978-3-319-29558-9

ISBN: 978-3-319-29557-2

Publisher: Springer International Publishing - Springer Journals

Mar 9, 2016

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Chapter 1Preliminaries on Lie groups

Fischer, Veronique; Ruzhansky, Michael

Pages: 15 –56

[In this chapter we provide the reader with basic preliminary facts about Lie groups that we will be using in the sequel. At the same time, it gives us a chance to fix the notation for the rest of the monograph. The topics presented here are all wellknown and we decided to give a brief account...
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Chapter 2Quantization on compact Lie groups

Fischer, Veronique; Ruzhansky, Michael

Pages: 57 –90

[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,...
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Chapter 3Homogeneous Lie groups

Fischer, Veronique; Ruzhansky, Michael

Pages: 91 –170

[By definition a homogeneous Lie group is a Lie group equipped with a family of dilations compatible with the group law. The abelian group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
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Chapter 4Rockland operators and Sobolev spaces

Fischer, Veronique; Ruzhansky, Michael

Pages: 171 –269

[In this chapter, we study a special type of operators: the (homogeneous) Rockland operators. These operators can be viewed as a generalisation of sub-Laplacians to the non-stratified but still homogeneous (graded) setting. The terminology comes from a property conjectured by Rockland and...
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Chapter 5Quantization on graded Lie groups

Fischer, Veronique; Ruzhansky, Michael

Pages: 271 –426

[In this chapter we develop the theory of pseudo-differential operators on graded Lie groups. Our approach relies on using positive Rockland operators, their fractional powers and their associated Sobolev spaces studied in Chapter 4. As we have pointed out in the introduction, the graded Lie...
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Chapter 6Pseudo-differential operators on the Heisenberg group

Fischer, Veronique; Ruzhansky, Michael

Pages: 427 –489

[The Heisenberg group was introduced in Example 1.6.4. It was our primal example of a stratified Lie group, see Section 3.1.1. Due to the importance of the Heisenberg group and of its many realisations, we start this chapter by sketching various descriptions of the Heisenberg group. We also...

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