Ehrenpreis, Leon 　著

内容

目次

PREFACE; CHAPTERS I-X; I. Introduction; I.1 Functions, Geometry andSpaces; I.2 Parametric Radon transform; I.3 Geometry of the nonparametricRadon transform; I.4 Parametrization problems; I.5 Differential equations;I.6 Lie groups; I.7 Fourier transform on varieties: The projection slicetheorem and the Poisson summation Formula; I.8 Tensor products and directintegrals; II. The nonparametric Radon transform; II.1 Radon transform andFourier transform; II.2 Tensor products and their topology; II.3 Supportconditions; III. Harmonic functions in Rn; III.1 Algebraic theory; III.2Analytic theory; III.3 Fourier series expansions on spheres; III.4 Fourierexpansions on hyperbolas; III.5 Deformation theory; IV. Harmonic functionsand Radon transform on algebraic varieties; IV.1 Algebraic theory and finiteCauchy problem; IV.2 The compact Watergate problem; IV.3 The noncompactWatergate problem; V. The nonlinear Radon and Fourier transforms; V.1Nonlinear Radon transform; V.2 Nonconvex support and regularity; V.3 Wavefront set; V.4 Microglobal analysis; VI. The parametric Radon transform; VI.1The John and invariance equations; VI.2 Characterization by John equations;VI.3 Non-Fourier analysis approach; VI.4 Some other parametric linear Radontransforms; VII. Radon transform on groups; VII.1 Affine and projectionmethods; VII.2 The nilpotent (horocyclic) Radon transform on G/K; VIII. Radontransform as the interrelation of geometry and analysis; VIII.1 Integralgeometry and differential equations; VIII.2 The Poisson summation formula andexotic intertwining; VIII.3 The Euler-MacLaurin summation formula; IX.Extension of solutions of differential equations; IX.1 Formulation of theproblem; IX.2 Hartogs-Lewy extension; IX.3 Wave front sets and the Caucyproblem; X. Periods of Eisenstein and Poincare series; X.1 The Lorentz group,Minowski geometry and a nonlinear projection-slice theorem; X.2 Spreads andcylindrical coordinates in Minowski geometry; X.3 Eisenstein series and theirperiods; X.4 Poincareseries and their periods; X.5 Hyperbolic Eisenstein andPoincare series; X.6 The four dimensional representation; X.7 Higherdimensional groups; BIBILIOGRAPHY OF CHAPTERS I-X; XI. Some problems ofintegral geometry arising in tomography; XI.1 Introduction; XI.2 X-raytomography; XI.3 Attenuated and exponential Radon transforms; XI.4 Hyperbolicintegral geometry and electrical impedance tomography; INDEX