Offbeat Integral Geometry on Symmetric Spaces

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

  • Covers over twenty years of extensive research on local aspects of integral geometry on symmetric spaces and the Heisenberg group in one condensed text 
  • Highlights significant and previously unpublished results
  • Includes numerous new problems
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  • ISBN 978-3-0348-0572-8
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Hardcover $149.00
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  • ISBN 978-3-0348-0571-1
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Softcover $149.00
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  • ISBN 978-3-0348-0800-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
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About this book

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 The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern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.

Reviews

From the reviews:

“The book presents a broad survey of the results in an interesting area, where the harmonic analysis and differential and integral equations interact in a fruitful way. The authors themselves have contributed a lot to the subject. The book will be interesting to those working in the border areas between analysis, integral geometry and Lie groups representation theory.” (Mark Agranovsky, Mathematical Reviews, March, 2014)

Table of contents (14 chapters)

  • Preliminaries

    Volchkov, Valery V. (et al.)

    Pages 3-42

  • The Euclidean Case

    Volchkov, Valery V. (et al.)

    Pages 43-83

  • Symmetric Spaces of the Non-compact Type

    Volchkov, Valery V. (et al.)

    Pages 85-110

  • Analogies for Compact Two-point Homogeneous Spaces

    Volchkov, Valery V. (et al.)

    Pages 111-134

  • The Phase Space Associated to the Heisenberg Group

    Volchkov, Valery V. (et al.)

    Pages 135-156

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0572-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-0348-0571-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-0348-0800-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Offbeat Integral Geometry on Symmetric Spaces
Authors
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0572-8
DOI
10.1007/978-3-0348-0572-8
Hardcover ISBN
978-3-0348-0571-1
Softcover ISBN
978-3-0348-0800-2
Edition Number
1
Number of Pages
X, 592
Topics