Offbeat Integral Geometry on Symmetric Spaces

  • Valery V. Volchkov
  • Vitaly V. Volchkov

Table of contents

  1. Front Matter
    Pages i-x
  2. Analysis on Symmetric Spaces

    1. Front Matter
      Pages 1-2
    2. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 3-42
    3. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 43-83
    4. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 85-110
    5. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 111-134
    6. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 135-156
  3. Offbeat Integral Geometry

    1. Front Matter
      Pages 157-158
    2. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 159-228
    3. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 229-264
    4. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 265-307
    5. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 309-357
    6. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 359-391
    7. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 393-433
    8. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 435-496
    9. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 497-526
    10. Valery V. Volchkov, Vitaly V. Volchkov
      Pages 527-555
  4. Back Matter
    Pages 557-592

About this book

Introduction

The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful in various fields of contemporary mathematics. The proofs given are “minimal” in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject.

Each chapter provides a historical perspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and the Heisenberg group, integral equations, special functions, and transmutation operators theory.

Keywords

Pompeiu property harmonic analysis on homogeneous spaces integral geometry mean periodicity symmetric spaces

Authors and affiliations

  • Valery V. Volchkov
    • 1
  • Vitaly V. Volchkov
    • 2
  1. 1., Department of MathematicsDonetsk National UniversityDonetskUkraine
  2. 2., Department of MathematicsDonetsk National UniversityDonetskUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0572-8
  • Copyright Information Springer Basel 2013
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0571-1
  • Online ISBN 978-3-0348-0572-8
  • About this book