Quantization on Nilpotent Lie Groups

Author:   Veronique Fischer ,  Michael Ruzhansky
Publisher:   Birkhauser Verlag AG
Edition:   1st ed. 2016
Volume:   314
ISBN:  

9783319295572


Pages:   557
Publication Date:   22 March 2016
Format:   Hardback
Availability:   In Print   Availability explained
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Quantization on Nilpotent Lie Groups


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Overview

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.

Full Product Details

Author:   Veronique Fischer ,  Michael Ruzhansky
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   1st ed. 2016
Volume:   314
Dimensions:   Width: 15.50cm , Height: 3.20cm , Length: 23.50cm
Weight:   9.753kg
ISBN:  

9783319295572


ISBN 10:   3319295578
Pages:   557
Publication Date:   22 March 2016
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

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.

Reviews

We want to remark that the contents of the volume are extremely rich. Beside presenting the new theory in the graded nilpotent case, the authors offer a complete view of the calculus of pseudo-differential operators on groups giving detailed references to preceding contributions. Also, we note the big effort to provide a self-contained presentation, addressed to a large audience. This monograph was the winner of the 2016 Ferran Sunyer i Balanguer prize. (Luigi Rodino, zbMATH 1347.22001, 2016)


Author Information

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).

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