Invariant random fields on spaces with a group action:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2013
|
| Schriftenreihe: | Probability and its applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben Weitere Ausgabe: Online-Ausg.: Invariant Random Fields on Spaces with a Group Action |
| Beschreibung: | XVII, 261 S. 24 cm |
| ISBN: | 9783642334054 3642334059 |
Internformat
MARC
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| 100 | 1 | |a Malyarenko, Anatoliy |d 1957- |0 (DE-588)1029493839 |4 aut | |
| 245 | 1 | 0 | |a Invariant random fields on spaces with a group action |c Anatoliy Malyarenko |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2013 | |
| 300 | |a XVII, 261 S. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Probability and its applications | |
| 500 | |a Literaturangaben | ||
| 500 | |a Weitere Ausgabe: Online-Ausg.: Invariant Random Fields on Spaces with a Group Action | ||
| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zufälliges Feld |0 (DE-588)4191094-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Zufälliges Feld |0 (DE-588)4191094-1 |D s |
| 689 | 0 | 1 | |a Spektraltheorie |0 (DE-588)4116561-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | |q application/pdf |u http://d-nb.info/1025198840/04 |3 Inhaltsverzeichnis | |
| 856 | 4 | |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=4101906&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-026245626 | |
Datensatz im Suchindex
| _version_ | 1806325819680751616 |
|---|---|
| adam_text |
IMAGE 1
1 INTRODUCTION 1
REFERENCES 7
2 SPECTRAL EXPANSIONS 9
2.1 RANDOM FIELDS 9
2.1.1 THE SCALAR CASE 9
2.1.2 THE VECTOR CASE 11
2.2 INVARIANT RANDOM FIELDS ON GROUPS 16
2.2.1 THE SCALAR CASE 16
2.2.2 THE VECTOR CASE 24
2.3 INVARIANT RANDOM FIELDS ON HOMOGENEOUS SPACES 28
2.3.1 THE SCALAR CASE 28
2.3.2 THE VECTOR CASE 37
2.4 INVARIANT RANDOM FIELDS ON GENERAL SPACES 46
2.4.1 THE SCALAR CASE 46
2.4.2 THE VECTOR CASE 55
2.5 ISOTROPIC RANDOM FIELDS ON COMMUTATIVE GROUPS 59
2.6 VOLTERRA ISOTROPIC RANDOM FIELDS 69
2.7 BIBLIOGRAPHICAL REMARKS 77
REFERENCES 83
3 L 2 THEORY OF INVARIANT RANDOM FIELDS 91
3.1 INVERSION FORMULAE 91
3.2 LINEAR DIFFERENTIAL EQUATIONS WITH RANDOM FIELDS 98
3.3 LINEAR FUNCTIONALS OF INVARIANT RANDOM FIELDS 102
3.4 BIBLIOGRAPHICAL REMARKS 112
REFERENCES 113
4 SAMPLE PATH PROPERTIES OF GAUSSIAN INVARIANT RANDOM FIELDS . . . . 1 1
5
4.1 INTRODUCTION 115
4.2 ELEMENTARY ABELIAN THEOREMS 116
4.2.1 THE COMPACT CASE 116
X I I I
HTTP://D-NB.INFO/1025198840
IMAGE 2
S
XJV CONTENTS
4.2.2 THE NONCOMPACT CASE 121
4.3 ADVANCED ABELIAN AND TAUBERIAN THEOREMS 125
4.3.1 THE COMPACT CASE 125
4.3.2 THE NONCOMPACT CASE 132
4.4 AN OPTIMAL SERIES EXPANSION OF THE MULTIPARAMETER FRACTIONAL
BROWNIAN MOTION 136
4.5 FUNCTIONAL LIMIT THEOREMS FOR THE MULTIPARAMETER FRACTIONAL BROWNIAN
MOTION 144
4.6 BIBLIOGRAPHICAL REMARKS 164
REFERENCES 165
5 APPLICATIONS 171
5.1 APPLICATIONS TO APPROXIMATION THEORY 171
5.2 APPLICATIONS TO COSMOLOGY 174
5.2.1 THE COSMIC MICROWAVE BACKGROUND (CMB) 174
5.2.2 THE PROBABILISTIC MODEL OF THE CMB 177
5.3 APPLICATIONS TO EARTHQUAKE ENGINEERING 191
5.4 BIBLIOGRAPHICAL REMARKS 198
REFERENCES 199
6 APPENDIX A: MATHEMATICAL BACKGROUND 203
6.1 DIFFERENTIAL GEOMETRY 203
6.1.1 MANIFOLDS 203
6.1.2 VECTOR BUNDLES 204
6.1.3 DIFFERENTIAL OPERATORS 206
6.1.4 INVARIANT DIFFERENTIAL OPERATORS ON MANIFOLDS 207
6.2 LIE GROUPS AND LIE ALGEBRAS 207
6.2.1 BASIC DEFINITIONS 207
6.2.2 SPHERICAL FUNCTIONS 210
6.3 GROUP ACTIONS AND GROUP REPRESENTATIONS 210
6.3.1 GROUP ACTIONS 210
6.3.2 POSITIVE-DEFINITE FUNCTIONS ON GROUPS AND GROUP REPRESENTATIONS
211
6.3.3 UNITARY REPRESENTATIONS OF COMMUTATIVE TOPOLOGICAL GROUPS 216
6.3.4 UNITARY REPRESENTATIONS OF COMPACT TOPOLOGICAL GROUPS . 219 6.3.5
THE FOURIER TRANSFORM 222
6.3.6 POSITIVE-DEFINITE FUNCTIONS ON HOMOGENEOUS SPACES AND INDUCED
REPRESENTATIONS 223
6.3.7 IRREDUCIBLE UNITARY REPRESENTATIONS OF LOW DIMENSIONAL NONCOMPACT
LIE GROUPS BY EXAMPLES 225
6.3.8 THE SPHERICAL FOURIER TRANSFORM 229
6.3.9 PALEY-WIENER THEOREMS 231
6.4 SPECIAL FUNCTIONS 232
6.4.1 THE GAMMA FUNCTION AND THE BETA FUNCTION 232
6.4.2 THE FOX H-FUNCTION 233
IMAGE 3
CONTENTS XV
6.4.3 HARMONICS 237
6.5 RIGGED HILBERT SPACES 241
6.6 ABELIAN AND TAUBERIAN THEOREMS 243
6.7 BIBLIOGRAPHICAL REMARKS 247
REFERENCES 250
INDEX 257 |
| any_adam_object | 1 |
| author | Malyarenko, Anatoliy 1957- |
| author_GND | (DE-588)1029493839 |
| author_facet | Malyarenko, Anatoliy 1957- |
| author_role | aut |
| author_sort | Malyarenko, Anatoliy 1957- |
| author_variant | a m am |
| building | Verbundindex |
| bvnumber | BV041272030 |
| classification_rvk | SK 800 |
| ctrlnum | (OCoLC)825943312 (DE-599)DNB1025198840 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041272030 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-03T00:55:40Z |
| institution | BVB |
| isbn | 9783642334054 3642334059 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026245626 |
| oclc_num | 825943312 |
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| owner | DE-19 DE-BY-UBM DE-11 DE-188 DE-83 |
| owner_facet | DE-19 DE-BY-UBM DE-11 DE-188 DE-83 |
| physical | XVII, 261 S. 24 cm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | Probability and its applications |
| spelling | Malyarenko, Anatoliy 1957- (DE-588)1029493839 aut Invariant random fields on spaces with a group action Anatoliy Malyarenko Berlin ; Heidelberg Springer 2013 XVII, 261 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Probability and its applications Literaturangaben Weitere Ausgabe: Online-Ausg.: Invariant Random Fields on Spaces with a Group Action Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Zufälliges Feld (DE-588)4191094-1 s Spektraltheorie (DE-588)4116561-5 s DE-604 application/pdf http://d-nb.info/1025198840/04 Inhaltsverzeichnis text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4101906&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026245626&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Malyarenko, Anatoliy 1957- Invariant random fields on spaces with a group action Spektraltheorie (DE-588)4116561-5 gnd Zufälliges Feld (DE-588)4191094-1 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4191094-1 |
| title | Invariant random fields on spaces with a group action |
| title_auth | Invariant random fields on spaces with a group action |
| title_exact_search | Invariant random fields on spaces with a group action |
| title_full | Invariant random fields on spaces with a group action Anatoliy Malyarenko |
| title_fullStr | Invariant random fields on spaces with a group action Anatoliy Malyarenko |
| title_full_unstemmed | Invariant random fields on spaces with a group action Anatoliy Malyarenko |
| title_short | Invariant random fields on spaces with a group action |
| title_sort | invariant random fields on spaces with a group action |
| topic | Spektraltheorie (DE-588)4116561-5 gnd Zufälliges Feld (DE-588)4191094-1 gnd |
| topic_facet | Spektraltheorie Zufälliges Feld |
| url | http://d-nb.info/1025198840/04 http://deposit.dnb.de/cgi-bin/dokserv?id=4101906&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026245626&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT malyarenkoanatoliy invariantrandomfieldsonspaceswithagroupaction |
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