Multivariate characteristic and correlation functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
2013
|
| Schriftenreihe: | De Gruyter studies in mathematics
50 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | IX, 366 S. graph. Darst. |
| ISBN: | 3110223988 9783110223989 9783111740447 |
Internformat
MARC
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| 100 | 1 | |a Sasvári, Zoltán |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Multivariate characteristic and correlation functions |c Zoltán Sasvári |
| 264 | 1 | |a Berlin |b De Gruyter |c 2013 | |
| 300 | |a IX, 366 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter studies in mathematics |v 50 | |
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| 689 | 0 | 1 | |a Korrelationsfunktion |0 (DE-588)4286297-8 |D s |
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
PREFACE V
1 CHARACTERISTIC FUNCTIONS 1
1.1 BASIC PROPERTIES 1
1.2 DIFFERENTIABILITY 9
1.3 INVERSION THEOREMS 18
1.4 BASIC PROPERTIES OF POSITIVE DEFINITE FUNCTIONS 25
1.5 FURTHER PROPERTIES O F POSITIVE DEFINITE FUNCTIONS ON 32
1.6 LEVY'S CONTINUITY THEOREM 38
1.7 THE THEOREMS O F BOCHNER AND HERGLOTZ 41
1.8 FOURIER TRANSFORMATION ON 47
1.9 FOURIER TRANSFORMATION ON DISCRETE COMMUTATIVE GROUPS 55
1.10 BASIC PROPERTIES OF GAUSSIAN DISTRIBUTIONS 57
1.11 SOME INEQUALITIES 61
2 CORRELATION FUNCTIONS 67
2.1 RANDOM FIELDS 67
2.2 CORRELATION FUNCTIONS O F SECOND ORDER RANDOM FIELDS 70
2.3 CONTINUITY AND DIFFERENTIABILITY 75
2.4 INTEGRATION WITH RESPECT TO COMPLEX MEASURES 77
2.5 THE KARHUNEN-LOEVE DECOMPOSITION 86
2.6 INTEGRATION WITH RESPECT TO ORTHOGONAL RANDOM MEASURES 92
2.7 THE THEOREM O F KARHUNEN 98
2.8 STATIONARY FIELDS 103
2.9 SPECTRAL REPRESENTATION O F STATIONARY FIELDS 109
2.10 UNITARY REPRESENTATIONS 117
2.11 UNITARY REPRESENTATIONS AND POSITIVE DEFINITE FUNCTIONS 125
3 SPECIAL PROPERTIES 132
3.1 STRICT POSITIVE DEFINITENESS 132
3.2 INFINITELY DIFFERENTIABLE AND RAPIDLY DECREASING FUNCTIONS 134
HTTP://D-NB.INFO/1028834101
IMAGE 2
VLLL
CONTENTS
3.3 ANALYTIC CHARACTERISTIC FUNCTIONS O F ONE VARIABLE 139
3.4 HOLOMORPHIC L 2 FOURIER TRANSFORMS 148
3.5 FURTHER PROPERTIES OF GAUSSIAN DISTRIBUTIONS 154
3.6 FOURIER TRANSFORMATION O F RADIAL MEASURES AND FUNCTIONS 160
3.7 RADIAL CHARACTERISTIC FUNCTIONS 165
3.8 SCHOENBERG'S THEOREMS ON RADIAL CHARACTERISTIC FUNCTIONS 172
3.9 CONVEX AND COMPLETELY MONOTONE FUNCTIONS 175
3.10 CONVOLUTION ROOTS WITH COMPACT SUPPORT 184
3.11 INFINITELY DIVISIBLE CHARACTERISTIC FUNCTIONS 187
3.12 CONDITIONALLY POSITIVE DEFINITE FUNCTIONS 189
4 THE EXTENSION PROBLEM 200
4.1 GENERAL RESULTS 200
4.2 THE CASES AND 7L D 208
4.3 DECOMPOSITION O F LOCALLY DEFINED POSITIVE DEFINITE FUNCTIONS 213
4.4 EXTENSION O F RADIAL POSITIVE DEFINITE FUNCTIONS 221
5 SELECTED APPLICATIONS 224
5.1 LIMIT THEOREMS 224
5.2 SUMS O F INDEPENDENT RANDOM VECTORS AND THE JESSEN-WINTNER PURITY
LAW 226
5.3 ERGODIC THEOREMS FOR STATIONARY FIELDS 234
5.4 FILTRATION OF DISCRETE STATIONARY FIELDS 239
APPENDIX 242
A BASIC NOTATION 242
A. 1 STANDARD NOTATION 242
A.2 MULTIDIMENSIONAL NOTATION 243
B BASIC ANALYSIS 244
B.L MISCELLANEOUS RESULTS FROM CLASSICAL ANALYSIS 244
B.2 UNIFORM CONVERGENCE O F CONTINUOUS FUNCTIONS 256
B.3 INFINITE PRODUCTS 261
B.4 CONVEX FUNCTIONS 264
B.5 THE RIEMANN-STIELTJES INTEGRAL 266
B.6 MULTIVARIATE CALCULUS 267
B.7 THE LEBESGUE INTEGRAL ON 272
IMAGE 3
CONTENTS IX
C ADVANCED ANALYSIS 278
C.L FUNCTIONS O F A COMPLEX VARIABLE 278
C.2 ALMOST PERIODIC FUNCTIONS 285
C.3 FOURIER SERIES 287
C.4 THE GAMMA FUNCTION AND THE FORMULAE O F STIRLING AND BINET 288
C.5 BESSEL FUNCTIONS 296
C.6 THE MELLIN TRANSFORM 300
C . L THE LAPLACE TRANSFORM 302
C.8 EXISTENCE OF CONTINUOUS LOGARITHMS 304
C.9 SOLUTIONS O F CERTAIN FUNCTIONAL EQUATIONS 306
C. 10 LINEAR INDEPENDENCE O F EXPONENTIAL FUNCTIONS 310
D FUNCTIONAL ANALYSIS 314
D.L INNER PRODUCT SPACES 314
D.2 MATRICES AND KERNELS 315
D.3 HILBERT SPACES AND LINEAR OPERATORS 327
D.4 CONVEX SETS AND THE THEOREM O F KREIN AND MILMAN 332
D.5 WEAK TOPOLOGIES 334
E MEASURE THEORY 339
E.L BOREL MEASURES, WEAK AND VAGUE CONVERGENCE 339
E.2 CONVOLUTION O F MEASURES AND FUNCTIONS 345
F PROBABILITY 347
F.L BASIC NOTIONS 347
F.2 CONVERGENCE O F RANDOM VECTORS 350
F.3 PRODUCTS O F PROBABILITY SPACES 352
F.4 CONDITIONAL EXPECTATION 354
BIBLIOGRAPHY 357
INDEX 361 |
| any_adam_object | 1 |
| author | Sasvári, Zoltán |
| author_facet | Sasvári, Zoltán |
| author_role | aut |
| author_sort | Sasvári, Zoltán |
| author_variant | z s zs |
| building | Verbundindex |
| bvnumber | BV040929173 |
| classification_rvk | SK 450 SK 800 |
| ctrlnum | (OCoLC)830890432 (DE-599)DNB1028834101 |
| dewey-full | 510 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 519 - Probabilities and applied mathematics |
| dewey-raw | 510 519.2 |
| dewey-search | 510 519.2 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040929173 |
| illustrated | Illustrated |
| indexdate | 2024-08-21T00:40:22Z |
| institution | BVB |
| isbn | 3110223988 9783110223989 9783111740447 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025908149 |
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| physical | IX, 366 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Sasvári, Zoltán Verfasser aut Multivariate characteristic and correlation functions Zoltán Sasvári Berlin De Gruyter 2013 IX, 366 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 50 Korrelationsfunktion (DE-588)4286297-8 gnd rswk-swf Charakteristische Funktion (DE-588)4147574-4 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Charakteristische Funktion (DE-588)4147574-4 s Korrelationsfunktion (DE-588)4286297-8 s Mehrere Variable (DE-588)4277015-4 s DE-604 Erscheint auch als Online-Ausgabe 978-3-11-022399-6 De Gruyter studies in mathematics 50 (DE-604)BV000005407 50 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4208578&prov=M&dok%5Fvar=1&dok%5Fext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025908149&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sasvári, Zoltán Multivariate characteristic and correlation functions De Gruyter studies in mathematics Korrelationsfunktion (DE-588)4286297-8 gnd Charakteristische Funktion (DE-588)4147574-4 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4286297-8 (DE-588)4147574-4 (DE-588)4277015-4 |
| title | Multivariate characteristic and correlation functions |
| title_auth | Multivariate characteristic and correlation functions |
| title_exact_search | Multivariate characteristic and correlation functions |
| title_full | Multivariate characteristic and correlation functions Zoltán Sasvári |
| title_fullStr | Multivariate characteristic and correlation functions Zoltán Sasvári |
| title_full_unstemmed | Multivariate characteristic and correlation functions Zoltán Sasvári |
| title_short | Multivariate characteristic and correlation functions |
| title_sort | multivariate characteristic and correlation functions |
| topic | Korrelationsfunktion (DE-588)4286297-8 gnd Charakteristische Funktion (DE-588)4147574-4 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | Korrelationsfunktion Charakteristische Funktion Mehrere Variable |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4208578&prov=M&dok%5Fvar=1&dok%5Fext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025908149&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT sasvarizoltan multivariatecharacteristicandcorrelationfunctions |