Verfügbarkeit: Fourier analysis in convex geometry

Fourier analysis in convex geometry:

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Bibliographische Detailangaben
1. Verfasser:	Koldobsky, Alexander 1955- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Providence, RI American Math. Soc. 2005
Schriftenreihe:	Mathematical surveys and monographs 116
Schlagworte:	Banach, Espaces de Convexe lichamen Ensembles convexes Fourier, Transformations de Fourier-analyse Convex sets Banach spaces Fourier transformations Banach-Raum Harmonische Analyse Konvexe Menge
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	VI, 170 S. graph. Darst.
ISBN:	0821837877

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MARC


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Datensatz im Suchindex

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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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isbn	0821837877
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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
volume_link	(DE-604)BV000018014
work_keys_str_mv	AT koldobskyalexander fourieranalysisinconvexgeometry

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