Offbeat integral geometry on symmetric spaces Valery V. Volchkov, Vitaly V. Volchkov

Format:

Book

Author/Creator:

Volchkov, V. V. (Valeri V.)

Contributor:

Volchkov, Vitaly V.

Language:

English

Subjects (All):

Symmetric spaces.

Integral geometry.

Fourier Analysis.

Medical Subjects:

Fourier Analysis.

Physical Description:

1 online resource

Place of Publication:

Basel Birkhäuser London Springer [distributor] 2013

System Details:

text file PDF

Summary:

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 The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern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

Contents:

Analysis on Symmetric Spaces Preliminaries The Euclidean Case Symmetric Spaces of the Non-compact Type Analogies for Compact Two-point Homogeneous Spaces The Phase Space Associated to the Heisenberg Group Offbeat Integral Geometry Functions with Zero Ball Means on Euclidean Space Two-radii Theorems in Symmetric Spaces The Problem of Findinga Function from Its Ball Means Sets with the Pompeiu Property Functions with Zero Integrals over Polytopes Ellipsoidal Means The Pompeiu Property on a Sphere The Pompeiu Transform on Symmetric Spaces and Groups Pompeiu Transforms on Manifolds

Notes:

Includes bibliographical references and indexes

Print version record

Other Format:

Print version Volchkov, V.V. (Valeri V.). Offbeat integral geometry on symmetric spaces

ISBN:

9783034805728

3034805721

OCLC:

826862637

Access Restriction:

Restricted for use by site license