The Radon transform:
"The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1999
|
| Edition: | 2. ed. |
| Series: | Progress in mathematics
5 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations. X-ray technology, nuclear magnetic resonance scanning, and tomography This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980."--BOOK JACKET |
| Physical Description: | XII, 188 S. Ill., graph. Darst. |
| ISBN: | 0817641092 3764341092 |
Staff View
MARC
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| 245 | 1 | 0 | |a The Radon transform |c Sigurdur Helgason |
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| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1999 | |
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| 490 | 1 | |a Progress in mathematics |v 5 | |
| 520 | 1 | |a "The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations. X-ray technology, nuclear magnetic resonance scanning, and tomography | |
| 520 | |a This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980."--BOOK JACKET | ||
| 650 | 4 | |a Radon, Transformations de | |
| 650 | 7 | |a Radon, Transformations de |2 ram | |
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Record in the Search Index
| _version_ | 1804127437950287872 |
|---|---|
| adam_text | SIGURDUR HELGASON THE RADON TRANSFORM SECOND EDITION BIRKHAUSER BOSTON *
BASEL * BERLIN CONTENTS PREFACE TO THE SECOND EDITION IX PREFACE TO THE
FIRST EDITION ... XI CHAPTER I THE RADON TRANSFORM ON R N 1.
INTRODUCTION 1 2. THE RADON TRANSFORM OF THE SPACES (! ) AND N ). THE
SUPPORT THEOREM 2 3. THE INVERSION FORMULA 15 4. THE PLANCHEREL FORMULA
20 5. RADON TRANSFORM OF DISTRIBUTIONS 22 6. INTEGRATION OVER D-PLANES.
X-RAY TRANSFORMS. THE RANGE OF THE D-PLANE TRANSFORM 28 7. APPLICATIONS
41 A) PARTIAL DIFFERENTIAL EQUATIONS 41 B) X-RAY RECONSTRUCTION 46
BIBLIOGRAPHICAL NOTES 51 CHAPTER II A DUALITY IN INTEGRAL GEOMETRY.
GENERALIZED RADON TRANSFORMS AND ORBITAL INTEGRALS 1. HOMOGENEOUS SPACES
IN DUALITY 53 2. THE RADON TRANSFORM FOR THE DOUBLE FIBRATION 57 3.
ORBITAL INTEGRALS 62 VI CONTENTS 4. EXAMPLES OF RADON TRANSFORMS FOR
HOMOGENEOUS SPACES IN DUALITY 63 A. THE FUNK TRANSFORM 63 B. THE X-RAY
TRANSFORM IN H 2 66 C. THE HOROCYCLES IN H 2 67 D. THE POISSON INTEGRAL
AS A RADON TRANSFORM 71 E. THE D-PLANE TRANSFORM 73 F. GRASSMANN
MANIFOLDS 74 G. HALF-LINES IN A HALF-PLANE 75 H. THETA SERIES AND CUSP
FORMS 79 BIBLIOGRAPHICAL NOTES 80 CHAPTER III THE RADON TRANSFORM ON
TWO-POINT HOMOGENEOUS SPACES 1. SPACES OF CONSTANT CURVATURE. INVERSION
AND SUPPORT THEOREMS 83 A. THE HYPERBOLIC SPACE 85 B. THE SPHERES AND
THE ELLIPTIC SPACES 93 C. THE SPHERICAL SLICE TRANSFORM 108 2. COMPACT
TWO-POINT HOMOGENEOUS SPACES. APPLICATIONS ILL 3. NONCOMPACT TWO-POINT
HOMOGENEOUS SPACES 118 4. THE X-RAY TRANSFORM ON A SYMMETRIC SPACE 119
5. MAXIMAL TORI AND MINIMAL SPHERES IN COMPACT SYMMETRIC SPACES 120
BIBLIOGRAPHICAL NOTES 122 CHAPTER IV ORBITAL INTEGRALS AND THE WAVE
OPERATOR FOR ISOTROPIC LORENTZ SPACES 1. ISOTROPIC SPACES 123 CONTENTS
VII A. THE RIEMANNIAN CASE 124 B. THE GENERAL PSEUDO-RIEMANNIAN CASE 124
C. THE LORENTZIAN CASE 128 2. ORBITAL INTEGRALS 128 3. GENERALIZED RIESZ
POTENTIALS 137 4. DETERMINATION OF A FUNCTION FROM ITS INTEGRALS OVER
LORENTZIAN SPHERES 140 5. ORBITAL INTEGRALS AND HUYGENS PRINCIPLE 144
BIBLIOGRAPHICAL NOTES 145 CHAPTER V FOURIER TRANSFORMS AND
DISTRIBUTIONS. A RAPID COURSE 1. THE TOPOLOGY OF THE SPACES P(R ), (R N
) AND 5(R N ) 147 2. DISTRIBUTIONS 149 3. THE FOURIER TRANSFORM 150 4.
DIFFERENTIAL OPERATORS WITH CONSTANT COEFFICIENTS 156 5. RIESZ
POTENTIALS 160 BIBLIOGRAPHICAL NOTES 168 BIBLIOGRAPHY 71 NOTATIONAL
CONVENTIONS 185 SUBJECT INDEX 187
|
| any_adam_object | 1 |
| author | Sigurður Helgason 1927-2023 |
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| author_facet | Sigurður Helgason 1927-2023 |
| author_role | aut |
| author_sort | Sigurður Helgason 1927-2023 |
| author_variant | s h sh |
| building | Verbundindex |
| bvnumber | BV012769707 |
| callnumber-first | Q - Science |
| callnumber-label | QA649 |
| callnumber-raw | QA649 |
| callnumber-search | QA649 |
| callnumber-sort | QA 3649 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 450 |
| ctrlnum | (OCoLC)41315440 (DE-599)BVBBV012769707 |
| dewey-full | 515/.723 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.723 |
| dewey-search | 515/.723 |
| dewey-sort | 3515 3723 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV012769707 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:33:21Z |
| institution | BVB |
| isbn | 0817641092 3764341092 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008683665 |
| oclc_num | 41315440 |
| open_access_boolean | |
| owner | DE-824 DE-355 DE-BY-UBR |
| owner_facet | DE-824 DE-355 DE-BY-UBR |
| physical | XII, 188 S. Ill., graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Sigurður Helgason 1927-2023 Verfasser (DE-588)123045762 aut The Radon transform Sigurdur Helgason 2. ed. Boston [u.a.] Birkhäuser 1999 XII, 188 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 5 "The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Solutions to such problems have a wide range of applications, namely to partial differential equations, group representations. X-ray technology, nuclear magnetic resonance scanning, and tomography This second edition, significantly expanded and updated, presents new material taking into account some of the progress made in the field since 1980."--BOOK JACKET Radon, Transformations de Radon, Transformations de ram Radon transforms Radon-Transformation (DE-588)4479199-9 gnd rswk-swf Radon-Transformierte (DE-588)4195862-7 gnd rswk-swf Radon-Transformation (DE-588)4479199-9 s DE-604 Radon-Transformierte (DE-588)4195862-7 s 1\p DE-604 Progress in mathematics 5 (DE-604)BV000004120 5 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008683665&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sigurður Helgason 1927-2023 The Radon transform Progress in mathematics Radon, Transformations de Radon, Transformations de ram Radon transforms Radon-Transformation (DE-588)4479199-9 gnd Radon-Transformierte (DE-588)4195862-7 gnd |
| subject_GND | (DE-588)4479199-9 (DE-588)4195862-7 |
| title | The Radon transform |
| title_auth | The Radon transform |
| title_exact_search | The Radon transform |
| title_full | The Radon transform Sigurdur Helgason |
| title_fullStr | The Radon transform Sigurdur Helgason |
| title_full_unstemmed | The Radon transform Sigurdur Helgason |
| title_short | The Radon transform |
| title_sort | the radon transform |
| topic | Radon, Transformations de Radon, Transformations de ram Radon transforms Radon-Transformation (DE-588)4479199-9 gnd Radon-Transformierte (DE-588)4195862-7 gnd |
| topic_facet | Radon, Transformations de Radon transforms Radon-Transformation Radon-Transformierte |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008683665&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT sigurðurhelgason theradontransform |