Spectral theory of dynamical systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Basel ; Boston ; Berlin
Birkhäuser
1998
|
| Series: | Birkhäuser advanced texts
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 182 S. |
| ISBN: | 3764358173 0817658173 |
Staff View
MARC
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| 100 | 1 | |a Nadkarni, Mahendra G. |d 1939- |e Verfasser |0 (DE-588)120671999 |4 aut | |
| 245 | 1 | 0 | |a Spectral theory of dynamical systems |c M. G. Nadkarni |
| 264 | 1 | |a Basel ; Boston ; Berlin |b Birkhäuser |c 1998 | |
| 300 | |a VII, 182 S. | ||
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Record in the Search Index
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| adam_text | Contents
Preface ix
1 The Hahn Hellinger Theorem
Definitions and the Problem 1
The Case of Multiplicity One, Cyclic Vector 2
Application to Second Order Stochastic Processes 4
Spectral Measures of Higher Multiplicity: A Canonical Example .... 6
Linear Operators Commuting with Multiplication 7
Spectral Type; Maximal Spectral Type 11
The Hahn Hellinger Theorem (First Form) 12
The Hahn Hellinger Theorem (Second Form) 14
Representation of Second Order Stochastic Processes 15
2 The Spectral Theorem for Unitary Operators
The Spectral Theorem: Multiplicity One Case 17
The Spectral Theorem: Higher Multiplicity Case 18
3 Symmetry and Denseness of the Spectrum
Spectrum U r It is Symmetric 21
Spectrum of Ut It is Dense 22
Examples 23
4 Multiplicity and Rank
A Theorem on Multiplicity 27
Approximation with Multiplicity N 28
Rank and Multiplicity 29
5 The Skew Product
The Skew Product: Definition and its Measure Preserving Property . . 33
The Skew Product: Its Spectrum 34
6 A Theorem of Helson and Parry
Statement of the Theorem 37
Weak von Neumann Automorphisms and Hyperfinite Actions 37
TheCocycleC(9,x) 38
The Random Cocycle and the Main Theorem 39
Remarks 43
vi Contents
7 Probability Measures on the Circle Group
Continuous Probability Measures on S1: They are Dense G$ 45
Measures Orthogonal to a Given Measure 46
Measures Singular Under Convolution And Folding 47
Rigid Measures 48
8 Baire Category Theorems of Ergodic Theory
Isometriesof LP{X,B,m) 51
Strong Topology on Isometries 52
Coarse and Uniform Topologies on G(m) 52
Baire Category of Classes of Unitary Operators 55
Baire Category of Classes of Non Singular Automorphisms 58
Baire Category of Classes of Measure Preserving Automorphisms ... 58
Baire Category and Joinings 59
9 Translations of Measures on the Circle
A Theorem of Weil and Mackey 63
The Sets A{y) and H^n) and Their Topologies 65
Groups Generated by Dense Subsets of A(fj,); Their Properties .... 67
Ergodic Measures on the Circle Group 68
A Theorem on Marginal Measures 71
10 B. Host s Theorem
Pairwise Independent and Independent Joinings of Automorphisms . . 75
B. Host s Theorem: The Statement 76
Mixing Implies Multiple Mixing if the Spectrum is Singular 76
B. Host s Theorem: The Proof 76
An Improvement and an Application 81
11 L°° Eigenvalues of Non Singular Automorphisms
The Group of Eigenvalues and Its Polish Topology 83
Quasi Invariance of the Spectrum 85
The Group e(T) is tr Compact 86
The Group e(T) is Saturated 87
12 Generalities on Systems of Imprimitivity
Spectral Measures and Group Actions 91
Cocycles; Systems of Imprimitivity 94
Irreducible Systems of Imprimitivity 95
Transitive Systems 96
Transitive Systems on R 96
Contents vii
13 Dual Systems of Imprimitivity
Compact Group Rotations; Dual Systems of Imprimitivity 99
Irreducible Dual Systems; Examples 100
The Group of Quasi Invariance; Its Topology 103
The Group of Quasi Invariance; It is an Eigenvalue Group 104
Extensions of Cocycles 105
14 Saturated Subgroups of the Circle Group
Saturated Subgroups of S1 109
Relation to Closures and Convex Hulls of Characters Ill
cr Compact Saturated Subgroups; Hi Groups 114
15 Riesz Products As Spectral Measures
Dissociated Trigonometric Polynomials 119
Classical Riesz Products and a Theorem of Peyriere 120
Riesz Products and Dynamics 122
Generalised Riesz Products 124
Maximal Spectral Types of Rank One Automorphisms 128
Examples and Remarks 131
The Non Singular Case, Proof of Theorem 15.18, and Further Remarks 133
Rank One Automorphisms: Their Group of Eigenvalues 135
Preliminary Calculations 135
The Functions yk 136
The Eigenvalue Group: Osikawa Criterion 138
Restatement of Theorem 15.50 139
The Eigenvalue Group: Structural Criterion 140
An Expression for ^,Q G e(T) 145
16 Additional Topics
Bounded Functions with Maximal Spectral Type 149
A Result on Mixing 151
A Result On Multiplicity 153
Combinatorial and Probabilistic Lemmas 155
Rank One Automorphisms by Construction 159
Ornstein s Class of Rank One Automorphisms 160
Mixing Rank One Automorphisms 162
References 171
Index 179
|
| any_adam_object | 1 |
| author | Nadkarni, Mahendra G. 1939- |
| author_GND | (DE-588)120671999 |
| author_facet | Nadkarni, Mahendra G. 1939- |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:22:25Z |
| institution | BVB |
| isbn | 3764358173 0817658173 |
| language | German |
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| physical | VII, 182 S. |
| publishDate | 1998 |
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| publisher | Birkhäuser |
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| spelling | Nadkarni, Mahendra G. 1939- Verfasser (DE-588)120671999 aut Spectral theory of dynamical systems M. G. Nadkarni Basel ; Boston ; Berlin Birkhäuser 1998 VII, 182 S. txt rdacontent n rdamedia nc rdacarrier Birkhäuser advanced texts Catégorie Baire Dynamique différentiable Dynamique différentiable ram Produit Riesz Spectre (Mathématiques) Théorie spectrale (Mathématiques) ram Differentiable dynamical systems Spectral theory (Mathematics) Dynamisches System (DE-588)4013396-5 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Spektraltheorie (DE-588)4116561-5 s DE-604 Ergodentheorie (DE-588)4015246-7 s Maßtheorie (DE-588)4074626-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008223350&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nadkarni, Mahendra G. 1939- Spectral theory of dynamical systems Catégorie Baire Dynamique différentiable Dynamique différentiable ram Produit Riesz Spectre (Mathématiques) Théorie spectrale (Mathématiques) ram Differentiable dynamical systems Spectral theory (Mathematics) Dynamisches System (DE-588)4013396-5 gnd Ergodentheorie (DE-588)4015246-7 gnd Spektraltheorie (DE-588)4116561-5 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4015246-7 (DE-588)4116561-5 (DE-588)4074626-4 |
| title | Spectral theory of dynamical systems |
| title_auth | Spectral theory of dynamical systems |
| title_exact_search | Spectral theory of dynamical systems |
| title_full | Spectral theory of dynamical systems M. G. Nadkarni |
| title_fullStr | Spectral theory of dynamical systems M. G. Nadkarni |
| title_full_unstemmed | Spectral theory of dynamical systems M. G. Nadkarni |
| title_short | Spectral theory of dynamical systems |
| title_sort | spectral theory of dynamical systems |
| topic | Catégorie Baire Dynamique différentiable Dynamique différentiable ram Produit Riesz Spectre (Mathématiques) Théorie spectrale (Mathématiques) ram Differentiable dynamical systems Spectral theory (Mathematics) Dynamisches System (DE-588)4013396-5 gnd Ergodentheorie (DE-588)4015246-7 gnd Spektraltheorie (DE-588)4116561-5 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Catégorie Baire Dynamique différentiable Produit Riesz Spectre (Mathématiques) Théorie spectrale (Mathématiques) Differentiable dynamical systems Spectral theory (Mathematics) Dynamisches System Ergodentheorie Spektraltheorie Maßtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008223350&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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