Hardy classes and operator theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press [u.a.]
1985
|
| Series: | Oxford mathematical monographs
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 161 S. |
| ISBN: | 0195035917 |
Staff View
MARC
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| 245 | 1 | 0 | |a Hardy classes and operator theory |c Marvin Rosenblum and James Rovnyak |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter 1. Shift Operators 1
1.1 Introduction 1
1.2 Partial Isometries 1
1.3 Wold Decomposition 2
1.4 Multiplicity 4
1.5 Universal Model 5
1.6 Analytic Operators 6
1.7 Inner Operators 7
1.8 Two Factorization Problems 8
1.9 Theorem. Solution of Problem 1 8
1.10 A Uniqueness Theorem 9
1.11 Counting Lemma 10
1.12 Beurling Lax Theorem 11
1.13 Lifting Theorem 12
1.14 Theorem. Abstract Form of the Lifting Theorem 12
1.15 Concrete Realization of a Shift Operator 15
Examples and Addenda 16
Notes 21
Chapter 2. Interpolation Theorems of the Pick Nevanlinna
and Loewner Types 22
2.1 Introduction 22
2.2 Nudel man s Problem 22
2.3 Main Theorem 23
2.4 The Pick and Pick Nevanlinna Theorems 25
2.5 Caratheodory Fejer Theorem 26
2.6 Simultaneous Generalization of the Pick Nevanlinna and Caratheodory
Fejer Theorems 27
2.7 Restrictions of Boundary Functions 30
2.8 Pick Class 34
2.9 Generalized Loewner Theorem 34
2.10 Hilbert Transforms 35
2.11 Equivalent Form of the Generalized Loewner Theorem 36
2.12 Real Valued Functions and Loewner s Theorem 37
2.13 Imaginary Functions and a Dual Result 39
Examples and Addenda 41
Notes 45
Chapter 3. Factorization of Toeplitz Operators 47
3.1 Introduction 47
3.2 Operator Matrices 48
3.3 Lowdenslager s Isometry 50
3.4 Theorem. Solution of the Abstract Szego Problem 50
3.5 Uniqueness Theorems 52
3.6 Theorem. Inner Outer Factorization of Toeplitz Operators 53
3.7 Theorem. Factorization of Nonnegative Invertible Toeplitz Operators 54
viii Contents
3.8 Comparison Theorem 54
3.9 Scalar Analytic Operators 55
3.10 Extremal Properties of Outer Operators 55
3.11 Proofs 56
Examples and Addenda 59
Notes 73
Chapter 4. Nevanlinna and Hardy Classes of Vector and
Operator Valued Functions 74
4.1 Introduction 74
4.2 Nevanlinna and Hardy Orlicz Classes 74
4.3 The Cases Q = D and IT; Characterizations of the Classes 77
4.4 Hardy Classes 79
4.5 The Cases X = CS and 8 {{£); Fatou s Theorem for Bounded Functions 81
4.6 Boundary Behavior of Functions of Bounded Type 84
4.7 Hardy Classes on the Disk 88
4.8 Hardy Classes on the Half Plane 90
Examples and Addenda 92
Notes 93
Chapter 5. Operator Valued Inner and Outer
Functions 94
5.1 Introduction 94
5.2 Inner and Outer Functions 94
5.3 The Subspace MJA) 96
5.4 The Subspace MOJF) 97
5.5 The Beurling Lax Theorem, Revisited 98
5.6 Theorem. Canonical Factorization of Functions of Bounded Type 99
5.7 Theorem. Canonical Factorization of Functions of Class JV+ 100
5.8 Uniqueness of Inner Outer Factorizations 101
5.9 Outer Functions on the Disk 101
5.10 Outer Functions on the Half Plane 104
Examples and Addenda 106
Notes 107
Chapter 6. Factorization of Nonnegative Operator
Valued Functions 109
6.1 Introduction 109
6.2 Toeplitz Operators and the Factorization of Nonnegative Operator
Valued Functions 110
6.3 Pseudomeromorphic Functions 113
6.4 Analyticity Across the Boundary 115
6.5 Theorem. Factorization of Pseudomeromorphic Functions 117
6.6 Operator Fejer Riesz Theorem 118
6.7 Theorem. Polynomials That Are Nonnegative on a Line 118
6.8 Rational Functions 119
6.9 Functions of Bounded Type; Mean Type 119
6.10 Entire Functions of Exponential Type 120
6.11 Operator Extension of Krein s Theorem 121
6.12 Krein Classes 123
6.13 Operator Extension of Ahiezer s Theorem 123
Contents ix
6.14 Theorem. Operator Extension of Szego s Theorem 124
Examples and Addenda 125
Notes 126
Appendix. Topics in Function Theory 128
1. Subharmonic Functions and the Class shl(D) 128
2. Theorem of Szego Solomentsev 132
3. Strongly Convex Functions and a Theorem of de la Vallee Poussin and
Nagumo 135
4. A Theorem of Flett and Kuran 136
5. A Theorem of M. G. Krein 139
6. Miscellaneous Theorems from Half Plane Function Theory 141
Bibliography 144
Author Index 157
Subject Index 159
|
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| id | DE-604.BV000548704 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:15:31Z |
| institution | BVB |
| isbn | 0195035917 |
| language | English |
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| physical | XII, 161 S. |
| psigel | TUB-www |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Oxford Univ. Press [u.a.] |
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| series2 | Oxford mathematical monographs |
| spelling | Rosenblum, Marvin Verfasser aut Hardy classes and operator theory Marvin Rosenblum and James Rovnyak Oxford [u.a.] Oxford Univ. Press [u.a.] 1985 XII, 161 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Operatortheorie (DE-588)4075665-8 gnd rswk-swf Hardy-Klasse (DE-588)4159107-0 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s Hardy-Klasse (DE-588)4159107-0 s DE-604 Rovnyak, James Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000337979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosenblum, Marvin Rovnyak, James Hardy classes and operator theory Operatortheorie (DE-588)4075665-8 gnd Hardy-Klasse (DE-588)4159107-0 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)4159107-0 |
| title | Hardy classes and operator theory |
| title_auth | Hardy classes and operator theory |
| title_exact_search | Hardy classes and operator theory |
| title_full | Hardy classes and operator theory Marvin Rosenblum and James Rovnyak |
| title_fullStr | Hardy classes and operator theory Marvin Rosenblum and James Rovnyak |
| title_full_unstemmed | Hardy classes and operator theory Marvin Rosenblum and James Rovnyak |
| title_short | Hardy classes and operator theory |
| title_sort | hardy classes and operator theory |
| topic | Operatortheorie (DE-588)4075665-8 gnd Hardy-Klasse (DE-588)4159107-0 gnd |
| topic_facet | Operatortheorie Hardy-Klasse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000337979&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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