The universality of the Radon transform:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
2003
|
| Edition: | 1. publ. |
| Series: | Oxford mathematical monographs
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 727 S. |
| ISBN: | 0198509782 |
Staff View
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Record in the Search Index
| _version_ | 1804129792035913728 |
|---|---|
| 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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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:10:46Z |
| institution | BVB |
| isbn | 0198509782 |
| language | English |
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| physical | XII, 727 S. |
| publishDate | 2003 |
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| spelling | Ehrenpreis, Leon 1930-2010 Verfasser (DE-588)122497961 aut The universality of the Radon transform Leon Ehrenpreis 1. publ. Oxford Clarendon Press 2003 XII, 727 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Radontransformatie gtt Radon transforms Radon-Transformation (DE-588)4479199-9 gnd rswk-swf Radon-Transformation (DE-588)4479199-9 s DE-604 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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 |
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