Buch, Englisch, 740 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1262 g
Buch, Englisch, 740 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1262 g
ISBN: 978-0-19-850978-3
Verlag: OUP Oxford
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.
The first part of the book discusses parametric and nonparametric Radon transforms, Harmonic Functions and Radon transform on Algebraic Varieties, nonlinear Radon and Fourier transforms, Radon transform on groups, and Radon transform as the interrelation of geometry and analysis. The later parts discuss the extension of solutions of differential equations, Periods of Eisenstein and Poincaré, and some problems of integral geometry arising in tomography. Examples and proofs are provided throughout the book to aid the reader's understanding.
This is the latest title in the Oxford Mathematical Monographs, which includes texts and monographs covering many topics of current research interest in pure and applied mathematics. Other titles include: Carbone and Semmes: A graphic apology for symmetry and implicitness; Higson and Roe: Analytic K-Homology; Iwaniec and Martin: Geometric Function Theory and Nonlinear Analysis; Lyons and Qian: System Control and Rough Paths. Also new in paperback Johnson and Lapidus: The Feynman Integral and Feynman's Operational Calculus; Donaldson and Kronheimer: The geometry of four-manifolds.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
Weitere Infos & Material
- Preface
- Chapters I-X
- 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 R^n
- 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/K
- VIII: Radon transform as the interrelation of geometry and analysis
- VIII.1 Integral geometry and differential equations
- VIII.2 The Poisson summation formula and exotic intertwining
- VIII.3 The Euler-MacLaurin summation formula
- IX: Extension of solutions of differential equations
- IX.1 Formulation of the problem
- IX.2 Hartogs-Lewy extension
- IX.3 Wave front sets and the Caucy problem
- X: Periods of Eisenstein and Poincaré series
- X.1 The Lorentz group, Minowski geometry and a nonlinear projection-slice theorem
- X.2 Spreads and cylindrical coordinates in Minowski geometry
- X.3 Eisenstein series and their periods
- X.4 Poincaréseries and their periods
- X.5 Hyperbolic Eisenstein and Poincaré series
- X.6 The four dimensional representation
- X.7 Higher dimensional groups
- Bibiliography of Chapters I-X
- XI: Peter Kuchment and Eric Todd Quinto: Some problems of integral geometry arising in tomography
- XI.1 Introduction
- XI.2 X-ray tomography
- XI.3 Attenuated and exponential Radon transforms
- XI.4 Hyperbolic integral geometry and electrical impedance tomography
- Index
