Overview
- 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
Part of the book series: Progress in Mathematics (PM, volume 314)
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Table of contents (6 chapters)
Keywords
About this book
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.
Reviews
“The main topic of this prize-winning monograph is the development of a pseudo-differential calculus on homogeneous Lie groups–the nilpotent Lie group equipped with a family of dilations compatible with the group structure. … It is really surprising that in spite of its great length and complicated subject, this book is very accessible.”(Antoni Wawrzyńczyk, Mathematical Reviews, April, 2017)
Authors and Affiliations
About the authors
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).
Bibliographic Information
Book Title: Quantization on Nilpotent Lie Groups
Authors: Veronique Fischer, Michael Ruzhansky
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-319-29558-9
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and the Author(s) 2016
Hardcover ISBN: 978-3-319-29557-2Published: 22 March 2016
Softcover ISBN: 978-3-319-80599-3Published: 20 April 2018
eBook ISBN: 978-3-319-29558-9Published: 08 March 2016
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XIII, 557
Number of Illustrations: 1 illustrations in colour
Topics: Topological Groups, Lie Groups, Abstract Harmonic Analysis, Functional Analysis, Mathematical Physics