Offbeat Integral Geometry on Symmetric Spaces

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 Heisenbe...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Volchkov, Valery V. (Author), Volchkov, Vitaly V. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Basel : Springer Basel : Imprint: Birkhäuser, 2013.
Edition:1st ed. 2013.
Subjects:
Special functions.
Harmonic analysis.
Mathematical analysis.
Geometry, Differential.
Special Functions.
Abstract Harmonic Analysis.
Integral Transforms and Operational Calculus.
Differential Geometry.
Online Access:Texto Completo
Table of Contents:
  • Preface
  • Part 1. Analysis on Symmetric Spaces. 1 Preliminaries
  • 2 The Euclidean case
  • 3 Symmetric spaces of the non-compact type.-4 Analogies for compact two-point homogeneous Spaces
  • 5 The phase space associated to the Heisenberg group.-Part 2. Offbeat Integral Geometry
  • 1 Functions with zero ball means on Euclidean space
  • 2 Two-radii theorems in symmetric spaces
  • 3 The problem of finding a function from its ball means
  • 4 Sets with the Pompeiu property
  • 5 Functions with zero integrals over polytopes.-6 Ellipsoidal means
  • 7 The Pompeiu property on a sphere
  • 8 The Pompeiu transform on symmetric spaces and groups.-9 Pompeiu transforms on manifolds
  • Bibliography
  • Index
  • Basic notation.

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