Quantization on Nilpotent Lie Groups

This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the a...

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Main Authors: Fischer, Veronique, Ruzhansky, Michael (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2016, 2016
Edition:1st ed. 2016
Series:Progress in Mathematics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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100 1 |a Fischer, Veronique 
245 0 0 |a Quantization on Nilpotent Lie Groups  |h Elektronische Ressource  |c by Veronique Fischer, Michael Ruzhansky 
250 |a 1st ed. 2016 
260 |a Cham  |b Springer International Publishing  |c 2016, 2016 
300 |a XIII, 557 p. 1 illus. in color  |b online resource 
505 0 |a Preface -- Introduction -- Notation and conventions -- 1 Preliminaries on Lie groups -- 2 Quantization on compact Lie groups -- 3 Homogeneous Lie groups -- 4 Rockland operators and Sobolev spaces -- 5 Quantization on graded Lie groups -- 6 Pseudo-differential operators on the Heisenberg group -- A Miscellaneous -- B Group C* and von Neumann algebras -- Schrödinger representations and Weyl quantization -- Explicit symbolic calculus on the Heisenberg group -- List of quantizations -- Bibliography -- Index 
653 |a Functional analysis 
653 |a Functional Analysis 
653 |a Harmonic analysis 
653 |a Lie groups 
653 |a Topological groups 
653 |a Topological Groups, Lie Groups 
653 |a Mathematical Physics 
653 |a Mathematical physics 
653 |a Abstract Harmonic Analysis 
653 |a Mathematics 
700 1 |a Ruzhansky, Michael  |e [author] 
710 2 |a SpringerLink (Online service) 
041 0 7 |a eng  |2 ISO 639-2 
989 |b Springer  |a Springer eBooks 2005- 
490 0 |a Progress in Mathematics 
856 |u http://dx.doi.org/10.1007/978-3-319-29558-9?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 512.482 
082 0 |a 512.55 
520 |a This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize