Quantization on Nilpotent Lie Groups

1. Auflage 2016
ISBN: 978-3-319-29557-2
Verlag: Springer International Publishing

Buch, Englisch, Band 314, 557 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1016 g

Reihe: Progress in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Ruzhansky, Michael

Fischer, Veronique

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

Veronique Fischer is a Senior Lecturer in Analysis at the University of Bath.

Michael Ruzhansky is a Professor of Pure Mathematics at Imperial College London.

The research of this monograph was supported by the 

EPSRC Grant EP/K039407/1 when Veronique Fischer was employed at

Imperial College London. It started when she was working at the

University of Padua. The work was also supported by the

Marie Curie FP7 project (PseudodiffOperatorS - 301599) and by

the Leverhulme Trust (grant RPG-2014-02).