Quantization on Nilpotent Lie Groups

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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/K[...] 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).

Zusammenfassung

First Open Access book in the Birkhäuser program

Contains a detailed and easy-to-follow exposition of nilpotent and homogeneous Lie groups and of homogeneous operators on such groups

Features a consistent development of the theory of Sobolev spaces on graded Lie groups

Gives a detailed development of the pseudo-differential analysis on graded Lie groups

The developed theory is thoroughly illustrated in the case of the Heisenberg group providing new links with various topics of analysis in this setting

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.

Details

Erscheinungsjahr:	2018
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Progress in Mathematics
Inhalt:	xiii 557 S. 1 farbige Illustr. 557 p. 1 illus. in color.
ISBN-13:	9783319805993
ISBN-10:	3319805991
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Fischer, Veronique Ruzhansky, Michael
Auflage:	Softcover reprint of the original 1st edition 2016
Hersteller:	Birkhäuser Palgrave Macmillan Springer International Publishing AG Progress in Mathematics
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	235 x 155 x 31 mm
Von/Mit:	Veronique Fischer (u. a.)
Erscheinungsdatum:	20.04.2018
Gewicht:	0,855 kg