TY  - BOOK
AU  - Fischer,Veronique
AU  - Ruzhansky,Michael
ED  - SpringerLink (Online service)
TI  - Quantization on Nilpotent Lie Groups
T2  - Progress in Mathematics,
SN  - 9783319295589
AV  - QA252.3 
U1  - 512.55 23
PY  - 2016///
CY  - Cham
PB  - Springer International Publishing, Imprint: Birkhäuser
KW  - Topological groups
KW  - Lie groups
KW  - Harmonic analysis
KW  - Functional analysis
KW  - Mathematical physics
KW  - Topological Groups, Lie Groups
KW  - Abstract Harmonic Analysis
KW  - Functional Analysis
KW  - Mathematical Physics
N1  - 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; Open Access
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-29558-9
ER  -