Offbeat Integral Geometry on Symmetric Spaces

• Main Authors: Volchkov, Valery V. (Author), Volchkov, Vitaly V. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhũser, 2013.
• Subjects: Mathematics.; Harmonic analysis.; Integral Transforms.; Functions, special.; Global differential geometry.; Special Functions.; Abstract Harmonic Analysis.; Integral Transforms, Operational Calculus.; Differential Geometry.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-0348-0572-8

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...

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.