Selected topics in the theory of spatial stationary flat processes:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Jena, Univ., Diss., 2001 |
| Physical Description: | II, 77, 5 S. 29 cm |
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MARC
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| 245 | 1 | 0 | |a Selected topics in the theory of spatial stationary flat processes |c von Evgueni Spodarev |
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Record in the Search Index
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| adam_text |
CONTENTS
INTRODUCTION 1
I STATIONARY FLAT PROCESSES 5
1 BASIC FACTS. 5
2 GRASSMANNIANS. 7
2.1 HYPERPLANES AND LINES. . 8
2.2 GRASSMANNIAN 7(2,4) AND ITS ISOMORPHISMS. 8
3 REPRESENTATIONS OF THE INTEGRAL KERNEL [,77]. 10
3.1 PARTICULAR CASES. 10
3.2 CRITICAL ANGLES. 11
3.3 MIXED VOLUMES. 14
II VARIATIONAL PROBLEMS 15
1 INTERSECTION DENSITY AND ISOPERIMETRIC PROBLEMS. 15
2 SOME HISTORICAL NOTES. 17
3 VARIATIONAL CALCULUS ON SIGNED MEASURES. 18
4 NECESSARY CONDITIONS OF MAXIMUM . 19
5 REMARKS AND OPEN PROBLEMS. 22
III INTEGRAL TRANSFORMS ' 25
1 GENERALIZED COSINE TRANSFORMS. 25
1.1 SPHERICAL COSINE AND SINE TRANSFORMS. 25
1.2 OPERATOR FAMILIES {TJ"} AND
{T*}
. 26
1.3 CONNECTION TO CONVEX AND STOCHASTIC GEOMETRY . 27
2 RADON TRANSFORMS.* . 28
2.1 RADON TRANSFORMS ON GRASSMANNIANS. 28
2.2 SPHERICAL RADON TRANSFORMS AND THEIR INVERSION . 28
2.3 USEFUL INTEGRAL AND DIFFERENTIAL RELATIONS. 30
3 INTEGRAL FORMULAE. 30
3.1 RADON TRANSFORMS OF THE POWER OF THE VOLUME. 31
3.2 DUAL RADON TRANSFORMS OF THE POWER OF THE VOLUME . . 36
3.3 CAUCHY - KUBOTA - TYPE FORMULAE FOR THE GENERALIZED
COSINE TRANSFORMS . 37
1
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/964244519
II
CONTENTS
3.4 DOUBLE FIBRATION FOR {T^} AND
{T^}. 38
3.5 BOUNDS FOR THE WEIGHTED IMAGES OF RADON TRANSFORMS . 40
IV AN INVERSE PROBLEM 43
1 THE ROSE OF INTERSECTIONS AND THE DIRECTIONAL DISTRIBUTION . 43
2 INVERSION FORMULAE FOR
K = D - 1, R = 1. 44
3 INVERSION FORMULAE FOR K = D - 1, 1 R ^ D - 1. 46
4 INVERSION VIA EXPANSIONS IN SPHERICAL HARMONICS. 47
5 CASE (7(2,4). 49
5.1 THE HAAR MEASURE ON (2,4). 49
5.2 THE FIRST PROOF OF THE THEOREM IV.5.1. 50
5.3 QUATERNIONS AND ROTATIONS IN K4 . 51
5.4 QUATEMIONIC COORDINATES FOR (2,4). 52
5.5 MECKE'S PROOF OF THEOREM IV.5.1 53
5.6 THE STRUCTURE OF
VF (2,4,0) 54X
6 REMARKS AND OPEN PROBLEMS. 59
V RELATED PROBLEMS 61
1 CHARACTERIZATION OF THE ROSES OF INTERSECTIONS. 61
1.1 PRELIMINARIES. 61
1.2 HYPERPLANE PROCESSES INTERSECTED WITH LINES. 62
2 ROSES OF NEIGHBORHOOD. 64
3 OPEN PROBLEMS. 66
BIBLIOGRAPHY 69
LIST OF SPECIAL SYMBOLS 76 |
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| indexdate | 2024-10-09T18:05:08Z |
| institution | BVB |
| language | English |
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| physical | II, 77, 5 S. 29 cm |
| publishDate | 2001 |
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| spelling | Spodarev, Evgenij 1975- Verfasser (DE-588)131480650 aut Selected topics in the theory of spatial stationary flat processes von Evgueni Spodarev 2001 II, 77, 5 S. 29 cm txt rdacontent n rdamedia nc rdacarrier Jena, Univ., Diss., 2001 Hochschulschrift gtt Schnittzahl gtt Stationärer Prozess gtt Stochastische Geometrie (DE-588)4133202-7 gnd rswk-swf Stationärer Prozess (DE-588)4056989-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Stochastische Geometrie (DE-588)4133202-7 s Stationärer Prozess (DE-588)4056989-5 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009824453&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Spodarev, Evgenij 1975- Selected topics in the theory of spatial stationary flat processes Hochschulschrift gtt Schnittzahl gtt Stationärer Prozess gtt Stochastische Geometrie (DE-588)4133202-7 gnd Stationärer Prozess (DE-588)4056989-5 gnd |
| subject_GND | (DE-588)4133202-7 (DE-588)4056989-5 (DE-588)4113937-9 |
| title | Selected topics in the theory of spatial stationary flat processes |
| title_auth | Selected topics in the theory of spatial stationary flat processes |
| title_exact_search | Selected topics in the theory of spatial stationary flat processes |
| title_full | Selected topics in the theory of spatial stationary flat processes von Evgueni Spodarev |
| title_fullStr | Selected topics in the theory of spatial stationary flat processes von Evgueni Spodarev |
| title_full_unstemmed | Selected topics in the theory of spatial stationary flat processes von Evgueni Spodarev |
| title_short | Selected topics in the theory of spatial stationary flat processes |
| title_sort | selected topics in the theory of spatial stationary flat processes |
| topic | Hochschulschrift gtt Schnittzahl gtt Stationärer Prozess gtt Stochastische Geometrie (DE-588)4133202-7 gnd Stationärer Prozess (DE-588)4056989-5 gnd |
| topic_facet | Hochschulschrift Schnittzahl Stationärer Prozess Stochastische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009824453&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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