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

  • Authors
  • Valery V. Volchkov
  • Vitaly V. Volchkov

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Symmetric Spaces. Harmonic Analysis on Spheres

    1. Front Matter
      Pages 1-3
    2. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 5-33
    3. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 61-83
    4. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 135-152
    5. Back Matter
      Pages 153-156
  3. Transformations with Generalized Transmutation Property Associated with Eigenfunctions Expansions

    1. Front Matter
      Pages 157-159
    2. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 161-176
    3. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 177-200
    4. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 201-229
    5. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 231-267
    6. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 269-334
    7. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 335-370
    8. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 371-394
    9. Back Matter
      Pages 395-399
  4. Mean Periodicity

    1. Front Matter
      Pages 401-403
    2. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 405-440
    3. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 441-486

About this book

Introduction

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.

Keywords

Convolution and transmutation operators Eigenfunction expansions Mean periodicity Spectral analysis and spectral synthesis Symmetric spaces and the Heisenberg group analysis harmonic analysis

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84882-533-8
  • Copyright Information Springer London 2009
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-84882-532-1
  • Online ISBN 978-1-84882-533-8
  • Series Print ISSN 1439-7382
  • About this book