Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group
Authors: Volchkov, Valery V., Volchkov, Vitaly V.
Free Preview 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
Buy this book
 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 tworadii 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 indepth, 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)


General Considerations
Pages 533

Analogues of the Beltrami–Klein Model for Rank One Symmetric Spaces of Noncompact Type
Pages 3560

Realizations of Rank One Symmetric Spaces of Compact Type
Pages 6183

Realizations of the Irreducible Components of the QuasiRegular Representation of Groups Transitive on Spheres. Invariant Subspaces
Pages 85134

NonEuclidean Analogues of Plane Waves
Pages 135152

Table of contents (21 chapters)
Recommended for you
Bibliographic Information
 Bibliographic Information

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

 Valery V. Volchkov
 Vitaly V. Volchkov
 Series Title
 Springer Monographs in Mathematics
 Copyright
 2009
 Publisher
 SpringerVerlag London
 Copyright Holder
 SpringerVerlag London
 eBook ISBN
 9781848825338
 DOI
 10.1007/9781848825338
 Hardcover ISBN
 9781848825321
 Softcover ISBN
 9781447122838
 Series ISSN
 14397382
 Edition Number
 1
 Number of Pages
 XI, 671
 Topics