The universality of the Radon transform / Leon Ehrenpreis.

Format:

Book

Author/Creator:

Ehrenpreis, Leon.

Series:

Oxford mathematical monographs.

Oxford science publications.

Oxford mathematical monographs

Oxford science publications

Language:

English

Subjects (All):

Radon transforms.

Physical Description:

1 online resource (740 p.)

Place of Publication:

Oxford : Clarendon Press ; New York : Oxford University Press, 2003.

Language Note:

English

Summary:

This monograph discusses the Radon transform, a field that has wide-ranging applications to X-ray technology, partial differential equations, nuclear magnetic resonance scanning, and tomography.

Contents:

Contents; 1 Introduction; 1.1 Functions, geometry, and spaces; 1.2 Parametric Radon transform; 1.3 Geometry of the nonparametric Radon transform; 1.4 Parametrization problems; 1.5 Differential equations; 1.6 Lie groups; 1.7 Fourier transform on varieties: The projection-slice theorem and the Poisson summation formula; 1.8 Tensor products and direct integrals; 2 The Nonparametric Radon transform; 2.1 Radon transform and Fourier transform; 2.2 Tensor products and their topology; 2.3 Support conditions; 3 Harmonic Functions in R(n); 3.1 Algebraic theory; 3.2 Analytic theory

3.3 Fourier series expansions on spheres3.4 Fourier expansions on hyperbolas; 3.5 Deformation theory; 3.6 Orbital integrals and Fourier transform; 4 Harmonic Functions and Radon Transform on Algebraic Varieties; 4.1 Algebraic theory and finite Cauchy problem; 4.2 The compact Watergate problem; 4.3 The noncompact Watergate problem; 5 The Nonlinear Radon and Fourier Transforms; 5.1 Nonlinear Radon transform; 5.2 Nonconvex support and regularity; 5.3 Wave front set; 5.4 Microglobal analysis; 6 The Parametric Radon Transform; 6.1 The John and invariance equations

6.2 Characterization by John equations6.3 Non-Fourier analysis approach; 6.4 Some other parametric linear Radon transforms; 7 Radon Transform on Groups; 7.1 Affine and projection methods; 7.2 The nilpotent (horocyclic) Radon transform on G/K; 7.3 Geodesic Radon transform; 8 Radon Transform as the Interrelation of Geometry and Analysis; 8.1 Integral geometry and differential equations; 8.2 The Poisson summation formula and exotic intertwining; 8.3 The Euler-Maclaurin summation formula; 8.4 The compact trick; 9 Extension of Solutions of Differential Equations; 9.1 Formulation of the problem

9.2 Hartogs-Lewy extension9.3 Wave front sets and the Cauchy problem; 9.4 Solutions of the Cauchy problem in a generalized sense; 9.5 Contact manifolds for partial differential equations; 10 Periods of Eisenstein and Poincaré series; 10.1 The Lorentz group, Minkowski geometry, and a nonlinear projection-slice theorem; 10.2 Spreads and cylindrical coordinates in Minkowski geometry; 10.3 Eisenstein series and their periods; 10.4 Poincaré series and their periods; 10.5 Hyperbolic Eisenstein and Poincaré series; 10.6 The four dimensional representation; 10.7 Higher dimensional groups

BibliographyAppendix: Some problems of integral geometry arising in tomography; A.1 Introduction; A.2 X-ray tomography; A.3 Attenuated and exponential Radon transforms; A.4 Hyperbolic integral geometry and electrical impedance tomography; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; X; Y; Z

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

9786611925000

0-19-152326-7

1-281-92500-4

OCLC:

302359632