Progress in Mathematics
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Quantization on Nilpotent Lie Groups

Authors: Fischer, Veronique, Ruzhansky, Michael V.

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  • 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
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  • ISBN 978-3-319-29558-9
  • This book is an open access book, you can download it for free on link.springer.com
Hardcover £44.99
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  • ISBN 978-3-319-29557-2
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Softcover £44.99
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  • ISBN 978-3-319-80599-3
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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.

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).

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)

“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)


Table of contents (6 chapters)

  • Preliminaries on Lie groups

    Fischer, Veronique (et al.)

    Pages 15-56

  • Quantization on compact Lie groups

    Fischer, Veronique (et al.)

    Pages 57-90

  • Homogeneous Lie groups

    Fischer, Veronique (et al.)

    Pages 91-170

  • Rockland operators and Sobolev spaces

    Fischer, Veronique (et al.)

    Pages 171-269

  • Quantization on graded Lie groups

    Fischer, Veronique (et al.)

    Pages 271-426

Buy this book

eBook  
  • ISBN 978-3-319-29558-9
  • This book is an open access book, you can download it for free on link.springer.com
Hardcover £44.99
price for United Kingdom (gross)
  • ISBN 978-3-319-29557-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover £44.99
price for United Kingdom (gross)
  • ISBN 978-3-319-80599-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Quantization on Nilpotent Lie Groups
Authors
Series Title
Progress in Mathematics
Series Volume
314
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
The Editor(s) (if applicable) and the Author(s)
eBook ISBN
978-3-319-29558-9
DOI
10.1007/978-3-319-29558-9
Hardcover ISBN
978-3-319-29557-2
Softcover ISBN
978-3-319-80599-3
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XIII, 557
Number of Illustrations
1 illustrations in colour
Topics