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 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, th…
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- Full title :Quantization on Nilpotent lie groups / Veronique Fischer, Michael Ruzhansky.
Summary
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.--Résumé de l'éditeur.
Read More ↓Edition Statements
- Publication Date:2016.
Publication Statements
- Publisher(s):Birkhäuser
- Place of Publication:Switzerland
- Language:eng
- Publication Date:2016.
Notes
Titre de l'écran-titre (visionné le 16 août 2016).
The Physical Object
- Description:1 ressource en ligne (xiii, 557 pages) : : illustrations en couleur, fichiers PDF
Edition Identifiers
- ISBN:9783319295589, 3319295586
- DOI:10.1007/978-3-319-29558-9
- oclc:on1132067528
- LC Classification:QA387
- Dewey Decimal:512/.482
Table of Contents
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.
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