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  • Produktbild: The Universality of the Radon Transform
  • Produktbild: The Universality of the Radon Transform

The Universality of the Radon Transform

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

02.10.2003

Abbildungen

numerous figures

Verlag

Oxford Academic

Seitenzahl

740

Maße (L/B/H)

24/16,1/4,4 cm

Gewicht

1262 g

Sprache

Englisch

ISBN

978-0-19-850978-3

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

02.10.2003

Abbildungen

numerous figures

Verlag

Oxford Academic

Seitenzahl

740

Maße (L/B/H)

24/16,1/4,4 cm

Gewicht

1262 g

Sprache

Englisch

ISBN

978-0-19-850978-3

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: The Universality of the Radon Transform
  • Produktbild: The Universality of the Radon Transform


    • 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 PoincarÃ(c) 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 PoincarÃ(c)series and their periods


    • X.5 Hyperbolic Eisenstein and PoincarÃ(c) 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