Fourier analysis in convex geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2005
|
| Series: | Mathematical surveys and monographs
116 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 170 S. graph. Darst. |
| ISBN: | 0821837877 |
Staff View
MARC
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Record in the Search Index
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| adam_text | MATHEMATICAL SURVEYS AND MONOGRAPHS VOLUME 116 FOURIER ANALYSIS IN
CONVEX GEOMETRY ALEXANDER KOLDOBSKY AMERICAN MATHEMATICAL SOCIETY
CONTENTS CHAPTER 1. INTRODUCTION 1 CHAPTER 2. BASIC CONCEPTS 13 2.1.
STAR BODIES 13 2.2. CONVEX BODIES 16 2.3. RADON TRANSFORMS 27 2.4. THE
GAMMA-FUNCTION 30 2.5. THE FOURIER TRANSFORM OF DISTRIBUTIONS 33 2.6.
FRACTIONAL DERIVATIVES 39 2.7. POSITIVE DEFINITE DISTRIBUTIONS 40 2.8.
STABLE RANDOM VARIABLES AND THE FUNCTION F Q 44 CHAPTER 3. VOLUME AND
THE FOURIER TRANSFORM 49 3.1. THE FIRST EXAMPLES: HYPERPLANE SECTIONS OF
G -BALLS 49 3.2. A GENERAL FORMULA FOR THE VOLUME OF HYPERPLANE
SECTIONS 53 3.3. THE PARALLEL SECTION FUNCTION AND THE FOURIER TRANSFORM
55 3.4. PARSEVAL S FORMULA ON THE SPHERE 62 3.5. REMARKS AND FURTHER
RESULTS 69 CHAPTER 4. INTERSECTION BODIES 71 4.1. A FOURIER ANALYTIC
CHARACTERIZATION 71 4.2. /C-INTERSECTION BODIES 75 4.3. LP-BALLS AS
^-INTERSECTION BODIES 80 4.4. THE SECOND DERIVATIVE TEST 85 4.5. REMARKS
AND FURTHER RESULTS 91 CHAPTER 5. THE BUSEMANN-PETTY PROBLEM 95 5.1. A
FOURIER ANALYTIC SOLUTION 95 5.2. HOW CAN ONE MAKE THE ANSWER
AFFIRMATIVE? 98 5.3. THE AFFIRMATIVE PART VIA SPHERICAL HARMONICS 100
5.4. ZVAVITCH S GENERALIZATION TO ARBITRARY MEASURES 105 5.5. REMARKS
AND FURTHER RESULTS 110 CHAPTER 6. INTERSECTION BODIES AND L P -SPACES
115 6.1. LP-SPACES AND POSITIVE DEFINITE FUNCTIONS 115 6.2. SCHOENBERG S
PROBLEMS ON POSITIVE DEFINITE FUNCTIONS 121 6.3. INTERSECTION BODIES AND
EMBEDDINGS IN L P , P 0 126 6.4. REMARKS AND FURTHER RESULTS 139
CHAPTER 7. EXTREMAL SECTIONS OF Q -BALLS 143 7.1. THE CASE OF THE
CUBE, K. BALL S THEOREM 143 VI CONTENTS 7.2. THE CASE 0 Q 2 147 7.3.
REMARKS AND FURTHER RESULTS 149 CHAPTER 8. PROJECTIONS AND THE FOURIER
TRANSFORM 151 8.1. A FORMULA FOR THE VOLUME OF HYPERPLANE PROJECTIONS
151 8.2. EXTREMAL HYPERPLANE PROJECTIONS OF G -BALLS 152 8.3.
PROJECTION BODIES 155 8.4. THE SHEPHARD PROBLEM 157 8.5. REMARKS AND
FURTHER RESULTS 161 BIBLIOGRAPHY 163 INDEX 169
|
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| indexdate | 2024-07-09T20:08:27Z |
| institution | BVB |
| isbn | 0821837877 |
| language | English |
| lccn | 2005041147 |
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| physical | VI, 170 S. graph. Darst. |
| publishDate | 2005 |
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| spelling | Koldobsky, Alexander 1955- (DE-588)137398182 aut Fourier analysis in convex geometry Alexander Koldobsky Providence, RI American Math. Soc. 2005 VI, 170 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 116 Banach, Espaces de Convexe lichamen gtt Ensembles convexes Fourier, Transformations de Fourier-analyse gtt Convex sets Banach spaces Fourier transformations Banach-Raum (DE-588)4004402-6 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Konvexe Menge (DE-588)4165212-5 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s Konvexe Menge (DE-588)4165212-5 s Banach-Raum (DE-588)4004402-6 s b DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1343-9 Mathematical surveys and monographs 116 (DE-604)BV000018014 116 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013212394&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koldobsky, Alexander 1955- Fourier analysis in convex geometry Mathematical surveys and monographs Banach, Espaces de Convexe lichamen gtt Ensembles convexes Fourier, Transformations de Fourier-analyse gtt Convex sets Banach spaces Fourier transformations Banach-Raum (DE-588)4004402-6 gnd Harmonische Analyse (DE-588)4023453-8 gnd Konvexe Menge (DE-588)4165212-5 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4023453-8 (DE-588)4165212-5 |
| title | Fourier analysis in convex geometry |
| title_auth | Fourier analysis in convex geometry |
| title_exact_search | Fourier analysis in convex geometry |
| title_full | Fourier analysis in convex geometry Alexander Koldobsky |
| title_fullStr | Fourier analysis in convex geometry Alexander Koldobsky |
| title_full_unstemmed | Fourier analysis in convex geometry Alexander Koldobsky |
| title_short | Fourier analysis in convex geometry |
| title_sort | fourier analysis in convex geometry |
| topic | Banach, Espaces de Convexe lichamen gtt Ensembles convexes Fourier, Transformations de Fourier-analyse gtt Convex sets Banach spaces Fourier transformations Banach-Raum (DE-588)4004402-6 gnd Harmonische Analyse (DE-588)4023453-8 gnd Konvexe Menge (DE-588)4165212-5 gnd |
| topic_facet | Banach, Espaces de Convexe lichamen Ensembles convexes Fourier, Transformations de Fourier-analyse Convex sets Banach spaces Fourier transformations Banach-Raum Harmonische Analyse Konvexe Menge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013212394&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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