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| Introduction | |
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| Functions, geometry, and spaces | |
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| Parametric Radon transform | |
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| Geometry of the nonparametric Radon transform | |
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| Parametrization problems | |
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| Differential equations | |
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| Lie groups | |
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| Fourier transform on varieties: The projection-slice theorem and the Poisson summation formula | |
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| Tensor products and direct integrals | |
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| The Nonparametric Radon transform | |
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| Radon transform and Fourier transform | |
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| Tensor products and their topology | |
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| Support conditions | |
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| Harmonic Functions in R[superscript n] | |
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| Algebraic theory | |
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| Analytic theory | |
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| Fourier series expansions on spheres | |
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| Fourier expansions on hyperbolas | |
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| Deformation theory | |
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| Orbital integrals and Fourier transform | |
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| Harmonic Functions and Radon Transform on Algebraic Varieties | |
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| Algebraic theory and finite Cauchy problem | |
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| The compact Watergate problem | |
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| The noncompact Watergate problem | |
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| The Nonlinear Radon and Fourier Transforms | |
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| Nonlinear Radon transform | |
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| Nonconvex support and regularity | |
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| Wave front set | |
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| Microglobal analysis | |
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| The Parametric Radon Transform | |
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| The John and invariance equations | |
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| Characterization by John equations | |
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| Non-Fourier analysis approach | |
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| Some other parametric linear Radon transforms | |
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| Radon Transform on Groups | |
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| Affine and projection methods | |
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| The nilpotent (horocyclic) Radon transform on G/K | |
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| Geodesic Radon transform | |
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| Radon Transform as the Interrelation of Geometry and Analysis | |
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| Integral geometry and differential equations | |
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| The Poisson summation formula and exotic intertwining | |
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| The Euler-Maclaurin summation formula | |
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| The compact trick | |
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| Extension of Solutions of Differential Equations | |
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| Formulation of the problem | |
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| Hartogs-Lewy extension | |
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| Wave front sets and the Cauchy problem | |
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| Solutions of the Cauchy problem in a generalized sense | |
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| Contact manifolds for partial differential equations | |
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| Periods of Eisenstein and Poincare series | |
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| The Lorentz group, Minkowski geometry, and a nonlinear projection-slice theorem | |
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| Spreads and cylindrical coordinates in Minkowski geometry | |
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| Eisenstein series and their periods | |
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| Poincare series and their periods | |
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| Hyperbolic Eisenstein and Poincare series | |
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| The four dimensional representation | |
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| Higher dimensional groups | |
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| Bibliography | |
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| Some problems of integral geometry arising in tomography | |
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| Introduction | |
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| X-ray tomography | |
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| Attenuated and exponential Radon transforms | |
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| Hyperbolic integral geometry and electrical impedance tomography | |
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| Index | |