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.
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.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
(Professor of Mathematics, Temple University, USA)
Inhaltsangabe
* 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
* 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
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