The Universality of the Radon Transform [Hardcover]

Written by a leading scholar in mathematics, 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. In this book, Ehrenpreis focuses on recent research and highlights the strong relationship between high-level pure mathematics and applications of the Radon transform to areas such as medical imaging.

PrefaceLeon Ehrenpreis
Chapters I-XLeon Ehrenpreis
I. Introduction
I.1 Functions, Geometry and Spaces
I.2 Parametric Radon transform
I.3 Geometry of the nonparametric Radon transform
I.4 Parametrization problems
I.5 Differential equations
I.6 Lie groups
I.7 Fourier transform on varieties: The projection slice theorem and the Poisson summation Formula
I.8 Tensor products and direct integrals
II. The nonparametric Radon transform
II.1 Radon transform and Fourier transform
II.2 Tensor products and their topology
II.3 Support conditions
III. Harmonic functions in Rn
III.1 Algebraic theory
III.2 Analytic theory
III.3 Fourier series expansions on spheres
III.4 Fourier expansions on hyperbolas
III.5 Deformation theory
IV. Harmonic functions and Radon transform on algebraic varieties
IV.1 Algebraic theory and finite Cauchy problem
IV.2 The compact Watergate problem
IV.3 The noncompact Watergate problem
V. The nonlinear Radon and Fourier transforms
V.1 Nonlinear Radon transform
V.2 Nonconvex support and regularity
V.3 Wave front set
V.4 Microglobal analysis
VI. The parametric Radon transform
VI.1 The John and invariance equations
VI.2 Characterization by John equations
VI.3 Non-Fourier analysis approach
VI.4 Some other parametric linear Radon transforms
VII. Radon transform on groups
VII.1 Affine and projection methods
VII.2 The nilpotent (horocyclic) Radon transform on G/l3^