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Springer Monographs in Mathematics

Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group

Authors: Volchkov, Valery V., Volchkov, Vitaly V.

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  • Deals with the subject in a systematic fashion
  • Most of the results give answers to questions that naturally arise and present the complete picture of corresponding phenomenon
  • Contains significant results published here for the first time
  • The proofs only involve concepts and facts which are indispensable to the essence of the subject
  • No other book features the same treatment of symmetric spaces
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eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-84882-533-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-1-84882-532-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA in USD
  • ISBN 978-1-4471-2283-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This book presents the first systematic and unified treatment of the theory of mean periodic functions on homogeneous spaces. This area has its classical roots in the beginning of the twentieth century and is now a very active research area, having close connections to harmonic analysis, complex analysis, integral geometry, and analysis on symmetric spaces.

The main purpose of this book is the study of local aspects of spectral analysis and spectral synthesis on Euclidean spaces, Riemannian symmetric spaces of an arbitrary rank and Heisenberg groups.  The subject can be viewed as arising from three classical topics: John's support theorem, Schwartz's fundamental principle, and Delsarte's two-radii theorem.

Highly topical, the book contains most of the significant recent results in this area with complete and detailed proofs. In order to make this book accessible to a wide audience, the authors have included an introductory section that develops analysis on symmetric spaces without the use of Lie theory. Challenging open problems are described and explained, and promising new research directions are indicated.

Designed for both experts and beginners in the field, the book is rich in methods for a wide variety of problems in many areas of mathematics.

Reviews

From the reviews:

“This book is devoted to some recent developments in the harmonic analysis of mean periodic functions on symmetric spaces and Heisenberg group … . Many topics appear here for the first time in book form. The book under review was written by two leading experts who have made extensive and deep contributions to the subject in the last fifteen years. … an in-depth, modern, clear exposition of the advanced theory of harmonic analysis on the symmetric domain of rank one and the Heisenberg group.” (Jingzhi Tie, Mathematical Reviews, Issue 2011 f)

“The book is a … comprehensive research monograph, based on the author’s work. … Each section contains an introduction, notes and remarks. The book presents a modern and ambitious theme of harmonic analysis. … will mainly attract experts.” (H. G. Feichtinger, Monatshefte für Mathematik, Vol. 163 (1), May, 2011)

“The book under review is a masterly treatise whose aim is to present the theory of mean periodic functions in symmetric spaces and on the Heisenberg group … . This book is for experts in geometric analysis. … of general interest to researchers in differential geometry, analysis and probability whose work wanders into symmetric spaces. It should certainly be in the library of every university where there is research in mathematics.” (Dave Applebaum, The Mathematical Gazette, Vol. 95 (534), November, 2011)


Table of contents (21 chapters)

Table of contents (21 chapters)
  • General Considerations

    Pages 5-33

    Volchkov, Prof. Valery V. (et al.)

  • Analogues of the Beltrami–Klein Model for Rank One Symmetric Spaces of Noncompact Type

    Pages 35-60

    Volchkov, Prof. Valery V. (et al.)

  • Realizations of Rank One Symmetric Spaces of Compact Type

    Pages 61-83

    Volchkov, Prof. Valery V. (et al.)

  • Realizations of the Irreducible Components of the Quasi-Regular Representation of Groups Transitive on Spheres. Invariant Subspaces

    Pages 85-134

    Volchkov, Prof. Valery V. (et al.)

  • Non-Euclidean Analogues of Plane Waves

    Pages 135-152

    Volchkov, Prof. Valery V. (et al.)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-84882-533-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.99
price for USA in USD
  • ISBN 978-1-84882-532-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA in USD
  • ISBN 978-1-4471-2283-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2009
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-84882-533-8
DOI
10.1007/978-1-84882-533-8
Hardcover ISBN
978-1-84882-532-1
Softcover ISBN
978-1-4471-2283-8
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XI, 671
Topics