Offbeat Integral Geometry On Symmetric Spaces Valery V Volchkov Vitaly V Volchkov by Valery V Volchkov; Vitaly V Volchkov 9783034805728, 3034805721 instant download after payment.

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 The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern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 reconst. Read more... Offbeat Integral Geometry on Symmetric Spaces; Contents; Preface; Part I Analysis on Symmetric Spaces; Chapter 1 Preliminaries; 1.1 Notation; 1.2 Distributions; 1.3 Some transcendental functions; 1.4 Spherical harmonics; 1.5 The Gegenbauer polynomials; 1.6 Exercises and further results; 1. The Titchmarsh theorem generalized (Voronin [V67]); 2. Discrete harmonics (Delsarte [D7]); 3. Spherical codes (Seidel [S10]); 4. The Kelvin transform (Axler-Bourdon-Ramey [A16]); Bibliographical notes; Chapter 2 The Euclidean Case; 2.1 Homeomorphisms with the generalized transmutation property 2.2 Some completeness results2.3 Systems of convolution equations; 2.4 Abel type integral equations; 2.5 Exercises and further results; 1. Relations between Abel operators and Hankel transforms; 2. Fractional integral operators (Koornwinder [K10]); 3. Integral equations; 4. A nonlinear Abel equation (Gorenflo and Vessella [G12]); 5. Support properties of Radon transforms on curves (Quinto [Q2]); Bibliographical notes; Chapter 3 Symmetric Spaces of the Non-compact Type; 3.1 Generalities; 3.2 The mapping; 3.3 Uniqueness theorems; 3.4 Exercises and further results; 1. The Jacobi transform Chapter 1 Functions with Zero Ball Means on Euclidean Space1.1 Simplest properties of functions with zero integrals over balls; 1.2 Uniqueness results; 1.3 Description of functions in the classes Vr(BR) and Ur(BR); 1.4 Local two-radii theorems; 1.5 Functions with zero integrals over balls in a spherical annulus; 1.6 The Liouville property; 1.7 Exercises and further results; 1. Continuation of functions with vanishing integrals over balls (Zaraisky [Z9]); 2. Uniqueness result (Zaraisky); 3. Decomposition of vector fields (Smith [S22])