Offbeat Integral Geometry on Symmetric Spaces

• Κύριοι συγγραφείς: Volchkov, Valery V. (Συγγραφέας), Volchkov, Vitaly V. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Springer Basel : Imprint: Birkhäuser, 2013.
• Θέματα: Mathematics.; Harmonic analysis.; Integral transforms.; Operational calculus.; Special functions.; Differential geometry.; Special Functions.; Abstract Harmonic Analysis.; Integral Transforms, Operational Calculus.; Differential Geometry.

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...

Πίνακας περιεχομένων:

• 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.