Gaussian processes, function theory, and the inverse spectral problem:
Gespeichert in:
Hauptverfasser: | , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York ; San Francisco ; London
Academic Press
1976
|
Schriftenreihe: | Probability and mathematical statistics
Volume 31 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | xi, 333 Seiten Illustrationen |
ISBN: | 0122264606 |
Internformat
MARC
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100 | 1 | |a Dym, Harry |d 1938- |0 (DE-588)124041205 |4 aut | |
245 | 1 | 0 | |a Gaussian processes, function theory, and the inverse spectral problem |c H. Dym: Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel ; H. P. McKean: Courant Institute of Mathematical Science, New York University, New York, New York |
264 | 1 | |a New York ; San Francisco ; London |b Academic Press |c 1976 | |
300 | |a xi, 333 Seiten |b Illustrationen | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a Probability and mathematical statistics |v Volume 31 | |
650 | 7 | |a Functietheorie |2 gtt | |
650 | 7 | |a Gauss-processen |2 gtt | |
650 | 4 | |a Processus gaussiens | |
650 | 4 | |a Processus stables | |
650 | 4 | |a Prévision, Théorie de la | |
650 | 4 | |a Spectre (Mathématiques) | |
650 | 7 | |a Stochastische processen |2 gtt | |
650 | 4 | |a Gaussian processes | |
650 | 4 | |a Prediction theory | |
650 | 4 | |a Spectral theory (Mathematics) | |
650 | 4 | |a Stationary processes | |
650 | 0 | 7 | |a Inverses Problem |0 (DE-588)4125161-1 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
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650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Gauß-Prozess |0 (DE-588)4156111-9 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
_version_ | 1807864680920645632 |
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adam_text |
Contents
Preface ix
Introduction l
Chapter 1 Background: Function Theory
1.1 Harmonic Functions 10
1.2 Positive Harmonic Functions on the Upper Half Plane 13
1.3 Analytic Functions of Exponential Type 16
1.4 Phragmen Lindelof Principle 17
1.5 Poisspn Jensen Formula 18
1.6 Quotients of Exponential Type 20
1.7 Carlson's Theorem 21
1.8 Hadamard Products 21
1.9 Nevanlinna's Formula 22
Chapter 2 Background: Hardy Functions
2.1 Fourier Integrals 26
2.2 Paley Wiener Theorem 28
2.3 Hardy Functions of Class H2 30
2.4 Projection 33
2.5 A Basis 34
2.6 An Inequality 35
2.7 Inner and Outer Functions 36
2.8 Tests for Outer Functions 39
2.9 Hardy Functions of Class H1 42
2.10 Hardy Functions of Class H* 46
2.11 Hilbert Transforms and Conjugate Functions 48
2.12 Phases 52
2.13 Inner Functions Again 53
2.14 Quasi Analytic Classes 55
Chapter 3 Background: Probability
3.1 Gaussian Families 61
3.2 Independence and Perpendicularity 63
3.3 Angles 65
3.4 Degree of Independence 67
3.5 Mutual Information 68
3.6 Kolmogorov's Modulus 69
vii
Viii CONTENTS
3.7 Stationary Gaussian Processes 71
3.8 Spectral Functions 74
3.9 Metric Transitivity 76
3.10 Ivankov's Alternative 78
Chapter 4 Past and Future
4.1 Kolmogorov Wiener Prediction Problem 82
4.2 Szego's Alternative 83
4.3 Doing the Prediction 87
4.4 Wiener's Formula 90
4.5 Filters and White Noise 92
4.6 Past and Future 96
4.7 Rational Spectral Densities 100
4.8 Type Spaces 108
4.9 Splitting 117
4.10 Germ and Gap 121
4.11 Okabe's Formulas 126
4.12 Mixing 130
4.13 Interpolation 136
Chapter 5 Strings and Spectral Functions
5.1 Strings 147
5.2 Self Adjoint Operators 153
5.3 Feller's Theorem 159
5.4 Green Functions 162
5.5 Principal Spectral Functions 176
5.6 Traces 181
5.7 Transforms 185
5.8 The Backwards Problem 194
5.9 Stieltjes' Investigations 203
5.10 Nonprincipal Spectral Functions 208
Chapter 6 Strings and Spaces of Integral Functions
6.1 De Branges Spaces 221
6.2 Short de Branges Spaces 228
6.3 Short Spaces and Short Strings 233
6.4 Type Spaces 241
6.5 Nesting of Short Spaces 247
6.6 Recovering the String 252
6.7 Hardy Densities 255
6.8 Dual Strings 262
6.9 Change of Scale and Mass 264
6.10 Prediction Using Part of the Past 279
6.11 Short Processes 291
6.12 A New Class of Strings 293
6.13 Strings for Interpolation 306
6.14 Interpolation: Examples 318
References 323
Index 329 |
any_adam_object | 1 |
author | Dym, Harry 1938- McKean, Henry P. 1930-2024 |
author_GND | (DE-588)124041205 (DE-588)130546275 |
author_facet | Dym, Harry 1938- McKean, Henry P. 1930-2024 |
author_role | aut aut |
author_sort | Dym, Harry 1938- |
author_variant | h d hd h p m hp hpm |
building | Verbundindex |
bvnumber | BV001963443 |
callnumber-first | Q - Science |
callnumber-label | QA274 |
callnumber-raw | QA274.4 |
callnumber-search | QA274.4 |
callnumber-sort | QA 3274.4 |
callnumber-subject | QA - Mathematics |
classification_rvk | SK 820 |
classification_tum | MAT 342f |
ctrlnum | (OCoLC)1601994 (DE-599)BVBBV001963443 |
dewey-full | 519.2 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.2 |
dewey-search | 519.2 |
dewey-sort | 3519.2 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Book |
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illustrated | Illustrated |
indexdate | 2024-08-20T00:35:13Z |
institution | BVB |
isbn | 0122264606 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001280430 |
oclc_num | 1601994 |
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physical | xi, 333 Seiten Illustrationen |
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spelling | Dym, Harry 1938- (DE-588)124041205 aut Gaussian processes, function theory, and the inverse spectral problem H. Dym: Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel ; H. P. McKean: Courant Institute of Mathematical Science, New York University, New York, New York New York ; San Francisco ; London Academic Press 1976 xi, 333 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Probability and mathematical statistics Volume 31 Functietheorie gtt Gauss-processen gtt Processus gaussiens Processus stables Prévision, Théorie de la Spectre (Mathématiques) Stochastische processen gtt Gaussian processes Prediction theory Spectral theory (Mathematics) Stationary processes Inverses Problem (DE-588)4125161-1 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Stationärer Prozess (DE-588)4056989-5 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Gauß-Prozess (DE-588)4156111-9 gnd rswk-swf Stationärer Prozess (DE-588)4056989-5 s DE-604 Funktionentheorie (DE-588)4018935-1 s Spektraltheorie (DE-588)4116561-5 s Inverses Problem (DE-588)4125161-1 s Gauß-Prozess (DE-588)4156111-9 s 1\p DE-604 McKean, Henry P. 1930-2024 (DE-588)130546275 aut Probability and mathematical statistics Volume 31 (DE-604)BV000892568 31 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280430&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Dym, Harry 1938- McKean, Henry P. 1930-2024 Gaussian processes, function theory, and the inverse spectral problem Probability and mathematical statistics Functietheorie gtt Gauss-processen gtt Processus gaussiens Processus stables Prévision, Théorie de la Spectre (Mathématiques) Stochastische processen gtt Gaussian processes Prediction theory Spectral theory (Mathematics) Stationary processes Inverses Problem (DE-588)4125161-1 gnd Spektraltheorie (DE-588)4116561-5 gnd Stationärer Prozess (DE-588)4056989-5 gnd Funktionentheorie (DE-588)4018935-1 gnd Gauß-Prozess (DE-588)4156111-9 gnd |
subject_GND | (DE-588)4125161-1 (DE-588)4116561-5 (DE-588)4056989-5 (DE-588)4018935-1 (DE-588)4156111-9 |
title | Gaussian processes, function theory, and the inverse spectral problem |
title_auth | Gaussian processes, function theory, and the inverse spectral problem |
title_exact_search | Gaussian processes, function theory, and the inverse spectral problem |
title_full | Gaussian processes, function theory, and the inverse spectral problem H. Dym: Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel ; H. P. McKean: Courant Institute of Mathematical Science, New York University, New York, New York |
title_fullStr | Gaussian processes, function theory, and the inverse spectral problem H. Dym: Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel ; H. P. McKean: Courant Institute of Mathematical Science, New York University, New York, New York |
title_full_unstemmed | Gaussian processes, function theory, and the inverse spectral problem H. Dym: Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel ; H. P. McKean: Courant Institute of Mathematical Science, New York University, New York, New York |
title_short | Gaussian processes, function theory, and the inverse spectral problem |
title_sort | gaussian processes function theory and the inverse spectral problem |
topic | Functietheorie gtt Gauss-processen gtt Processus gaussiens Processus stables Prévision, Théorie de la Spectre (Mathématiques) Stochastische processen gtt Gaussian processes Prediction theory Spectral theory (Mathematics) Stationary processes Inverses Problem (DE-588)4125161-1 gnd Spektraltheorie (DE-588)4116561-5 gnd Stationärer Prozess (DE-588)4056989-5 gnd Funktionentheorie (DE-588)4018935-1 gnd Gauß-Prozess (DE-588)4156111-9 gnd |
topic_facet | Functietheorie Gauss-processen Processus gaussiens Processus stables Prévision, Théorie de la Spectre (Mathématiques) Stochastische processen Gaussian processes Prediction theory Spectral theory (Mathematics) Stationary processes Inverses Problem Spektraltheorie Stationärer Prozess Funktionentheorie Gauß-Prozess |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280430&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV000892568 |
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