Holdings: The universality of the Radon transform

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Bibliographic Details
Title:	The universality of the Radon transform
From:	Leon Ehrenpreis
Person:	Ehrenpreis, Leon 1930-2010 Verfasser aut
Main Author:	Ehrenpreis, Leon 1930-2010 (Author)
Format:	Book
Language:	English
Published:	Oxford Clarendon Press 2003
Edition:	1. publ.
Series:	Oxford mathematical monographs
Notation:	SK 450
Subjects:	Radontransformatie Radon transforms Radon-Transformation
Online Access:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010177397&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XII, 727 S.
ISBN:	0198509782

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MARC


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Record in the Search Index

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adam_text	CONTENTS 1 Introduction 1 1.1 Functions, geometry, and spaces 2 1.2 Parametric Radon transform 31 1.3 Geometry of the nonparametric Radon transform 37 1.4 Parametrization problems 44 1.5 Differential equations 56 1.6 Lie groups 71 1.7 Fourier transform on varieties: The projection slice theorem and the Poisson summation formula 87 1.8 Tensor products and direct integrals 103 2 The Nonparametric Radon transform 112 2.1 Radon transform and Fourier transform 112 2.2 Tensor products and their topology 139 2.3 Support conditions 152 3 Harmonic Functions in Rn 161 3.1 Algebraic theory 161 3.2 Analytic theory 193 3.3 Fourier series expansions on spheres 211 3.4 Fourier expansions on hyperbolas 230 3.5 Deformation theory 246 3.6 Orbital integrals and Fourier transform 249 4 Harmonic Functions and Radon Transform on Algebraic Varieties 253 4.1 Algebraic theory and finite Cauchy problem 253 4.2 The compact Watergate problem 274 4.3 The noncompact Watergate problem 294 5 The Nonlinear Radon and Fourier Transforms 299 5.1 Nonlinear Radon transform 299 5.2 Nonconvex support and regularity 315 5.3 Wave front set 333 5.4 Microglobal analysis 358 6 The Parametric Radon Transform 364 6.1 The John and invariance equations 364 6.2 Characterization by John equations 381 xii Contents 6.3 Non Fourier analysis approach 404 6.4 Some other parametric linear Radon transforms 410 7 Radon Transform on Groups 416 7.1 Affine and projection methods 416 7.2 The nilpotent (horocyclic) Radon transform on G/K 420 7.3 Geodesic Radon transform 465 8 Radon Transform as the Interrelation of Geometry and Analysis 474 8.1 Integral geometry and differential equations 474 8.2 The Poisson summation formula and exotic intertwining 483 8.3 The Euler Maclaurin summation formula 496 8.4 The compact trick 503 9 Extension of Solutions of Differential Equations 511 9.1 Formulation of the problem 511 9.2 Hartogs Lewy extension 517 9.3 Wave front sets and the Cauchy problem 533 9.4 Solutions of the Cauchy problem in a generalized sense 552 9.5 Contact manifolds for partial differential equations 572 10 Periods of Eisenstein and Poincare series 580 10.1 The Lorentz group, Minkowski geometry, and a nonlinear projection slice theorem 580 10.2 Spreads and cylindrical coordinates in Minkowski geometry 591 10.3 Eisenstein series and their periods 601 10.4 Poincare series and their periods 630 10.5 Hyperbolic Eisenstein and Poincare series 642 10.6 The four dimensional representation 648 10.7 Higher dimensional groups 663 Bibliography 671 Appendix Some problems of integral geometry arising in tomography 681 A.I Introduction 681 A.2 X ray tomography 681 A.3 Attenuated and exponential Radon transforms 693 A.4 Hyperbolic integral geometry and electrical impedance tomography 710 Index 723
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indexdate	2024-12-20T11:11:50Z
institution	BVB
isbn	0198509782
language	English
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spellingShingle	Ehrenpreis, Leon 1930-2010 The universality of the Radon transform Radontransformatie gtt Radon transforms Radon-Transformation (DE-588)4479199-9 gnd
subject_GND	(DE-588)4479199-9
title	The universality of the Radon transform
title_auth	The universality of the Radon transform
title_exact_search	The universality of the Radon transform
title_full	The universality of the Radon transform Leon Ehrenpreis
title_fullStr	The universality of the Radon transform Leon Ehrenpreis
title_full_unstemmed	The universality of the Radon transform Leon Ehrenpreis
title_short	The universality of the Radon transform
title_sort	the universality of the radon transform
topic	Radontransformatie gtt Radon transforms Radon-Transformation (DE-588)4479199-9 gnd
topic_facet	Radontransformatie Radon transforms Radon-Transformation
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010177397&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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