Topics in Hardy classes and univalent functions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel ; Boston, Mass. ; Berlin
Birkhäuser Verlag
1994
|
| Series: | Birkhäuser Advanced Texts
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seiten 237 - 244 |
| Physical Description: | IX, 250 Seiten graph. Darst. |
| ISBN: | 376435111X 081765111X |
Staff View
MARC
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| 100 | 1 | |a Rosenblum, Marvin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Topics in Hardy classes and univalent functions |c Marvin Rosenblum, James Rovnyak |
| 264 | 1 | |a Basel ; Boston, Mass. ; Berlin |b Birkhäuser Verlag |c 1994 | |
| 300 | |a IX, 250 Seiten |b graph. Darst. | ||
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| 490 | 0 | |a Birkhäuser Advanced Texts | |
| 500 | |a Literaturverzeichnis Seiten 237 - 244 | ||
| 650 | 4 | |a Fonctions univalentes | |
| 650 | 7 | |a Fonctions univalentes |2 ram | |
| 650 | 4 | |a Hardy, Classes de | |
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| 650 | 7 | |a Univalente functies |2 gtt | |
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| 650 | 7 | |a espace Hardy |2 inriac | |
| 650 | 7 | |a fonction harmonique |2 inriac | |
| 650 | 7 | |a fonction sous-harmonique |2 inriac | |
| 650 | 7 | |a fonction univalente |2 inriac | |
| 650 | 7 | |a théorie opérateur |2 inriac | |
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Record in the Search Index
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Contents
Preface xi
Notation xii
Chapter 1
Harmonic Functions
1.1 Introduction 1
1.2 Uniqueness principle 2
1.3 The Poisson kernel 3
1.4 Normalized Lebesgue measure 4
1.5 Dirichlet problem for the unit disk 4
1.6 Properties of harmonic functions 6
1.7 Mean value property 8
1.8 Harnack's theorem 8
1.9 Weak compactness principle 10
1.10 Nonnegative harmonic functions 11
1.11 Herglotz and Riesz representation theorem 11
1.12 Stieltjes inversion formula 12
1.13 Integral of the Poisson kernel 12
1.14 Examples 13
1.15 Space hl{D) 14
1.16 Characterization of hl{D) 14
1.17 Nontangential convergence 14
1.18 Fatou's theorem 15
1.19 Boundary functions 18
Examples and addenda 18
Chapter 2
Subharmonic Functions
2.1 Introduction 23
2.2 Upper semicontinuous functions 23
2.3 Subharmonic functions 25
2.4 Some properties of subharmonic functions 26
2.5 Maximum principle 27
2.6 Convergence of mean values 28
2.7 Convex functions 29
2.8 Structure of convex functions 29
2.9 Jensen's inequality 31
2.10 Composition of convex and subharmonic functions 31
2.11 Vector and operator valued functions 32
2.12 Subharmonic functions from holomorphic functions 32
vi Contents
Chapter 3
Part I. Harmonic Majorants
3.1 Introduction 35
3.2 Least harmonic majorant 35
3.3 Existence of least harmonic majorants .: 36
3.4 Construction of harmonic majorants 36
3.5 Class sh^D) 38
3.6 Characterization of sh1 (D) 38
3.7 Absolutely continuous component of a related measure 40
3.8 Uniformly integrable family 41
3.9 Strongly convex functions 41
3.10 Theorem of de la Vallee Poussin and Nagumo 42
3.11 Singular component of associated measures 45
3.12 Sufficient conditions for absolute continuity 46
3.13 Theorem of Szego Solomentsev 47
3.14 Remark 48
Part II. Nevanlinna and Hardy Orlicz Classes
3.15 Hardy and Nevanlinna classes 48
3.16 Linearity of the classes 49
3.17 Properties of log+ x 49
3.18 Majorants for strongly convex functions 49
3.19 Compositions and restrictions 51
3.20 Quotients of bounded functions 51
Examples and addenda 52
Chapter 4
Hardy Spaces on the Disk
4.1 Introduction 55
4.2 Inner and outer functions 55
4.3 Rational inner functions 57
4.4 Infinite products 58
4.5 An infinite product 59
4.6 Blaschke products 60
4.7 Inner functions with no zeros 61
4.8 Singular inner functions 61
4.9 Factorization of inner functions 61
4.10 Boundary functions for N{D) 63
4.11 Characterization of N{D) 63
4.12 Condition on zeros 64
4.13 N{D) as an algebra 64
Contents vii
4.14 Characterization of N+(D) 65
4.15 N+(D) as an algebra 66
4.16 Estimates from boundary functions for N+(D) 66
4.17 Outer functions in N+(D) 66
4.18 Characterization of Sjv(D) 67
4.19 Nevanlinna and Hardy Orlicz classes on the boundary 70
4.20 Szego's problem 70
4.21 Classes HP(D) and HP(T) 70
4.22 Characterization of HP(D) 71
4.23 Characterization of HP(T) 71
4.24 Connection between HP(D) and Hp{r) 72
4.25 Hp{T) as a subspace of LP(T) 72
4.26 Hp(D) and HP(T) as Banach spaces 73
4.27 F. and M. Riesz theorem 74
4.28 H2{D) and H2(F) 74
4.29 Sufficient conditions for outer functions 75
4.30 Beurling's theorem 76
4.31 Theorem of Szego, Kolmogorov, and Krem 77
4.32 Closure of trigonometric functions in Lp(/j.) 80
Chapter 5
Function Theory on a Half Plane
5.1 Introduction 81
5.2 Poisson representation 83
5.3 Nevanlinna representation 84
5.4 Stieltjes inversion formula 84
5.5 Fatou's theorem 86
5.6 Boundary functions for N(U) 87
5.7 Limits of nondecreasing functions 88
5.8 Nonnegative harmonic functions 88
5.9 Theorem of Flett and Kuran 89
5.10 Nevanlinna and Hardy Orlicz classes 91
5.11 Notation and terminology 91
5.12 Szego's problem on the line 92
5.13 Inner and outer functions 92
5.14 Examples and miscellaneous properties 94
5.15 Hardy classes 95
5.16 Characterization of Sjp(U) 95
5.17 Inclusions among classes 96
5.18 Poisson representation for 9jp{U) 96
5.19 Cauchy representation for HP{U) 96
viii Contents
5.20 Characterization of HP(U) 98
5.21 #P(II) as a subspace of N+(ll) 98
5.22 Condition for mean convergence 98
5.23 Hp(Tl) and Sjp(H) as subspaces of N+(U) 100
5.24 Hp\li) and Sjp(W) as Banach spaces 101
5.25 Local convergence to a boundary function 102
5.26 Remark on the definition of HP(U) 103
5.27 Plancherel theorem 104
5.28 Paley Wiener representation 104
5.29 Natural isomorphisms 105
5.30 Hilbert transforms 106
5.31 Real and imaginary parts of boundary functions 108
5.32 Cauchy transform on Lp(—oo, oo) 108
5.33 Mapping / / if on Lp( oo, oo) to HP(R) 110
5.34 M. Riesz theorem Ill
5.35 Algebraic properties of Hilbert transforms Ill
Examples and addenda Ill
Chapter 6
Phragmen Lindelof Principle
6.1 Introduction 117
6.2 Phragmen Lindelof principle 117
6.3 Functions on a sector 118
6.4 Estimate from behavior on the imaginary axis 119
6.5 Blaschke products on the imaginary axis 120
6.6 Equivalence of the unit disk and a half disk 121
6.7 Function theory on a half disk 123
6.8 Estimates on a half disk 124
6.9 Test to belong to N(U) 125
6.10 Asymptotic behavior of Poisson integrals 125
6.11 Estimate from behavior on semicircles 127
6.12 Blaschke products on semicircles 128
6.13 Factorization of bounded type functions 128
6.14 Nevanlinna factorization and mean type 129
6.15 Formulas for mean type 130
6.16 Exponential type 131
6.17 Krem's theorem 131
6.18 Inequalities for mean type 133
Examples and addenda 134
Contents ix
Chapter 7
Loewner Families
7.1 Definitions and overview of the subject 137
7.2 Preliminary results 143
7.3 Riemann mapping theorem 148
7.4 The Dirichlet space and area theorem 150
7.5 Generalization of the Dirichlet space 152
7.6 Bieberbach's theorem 160
7.7 Size of the image domain 163
7.8 Distortion theorem 164
7.9 Caratheodory convergence theorem 168
7.10 Subordination 174
7.11 Technical lemmas 175
7.12 Parametric representation of Loewner families 180
Chapter 8
Loewner's Differential Equation
8.1 Loewner families and associated semigroups 181
8.2 Estimates derived from Schwarz's lemma 185
8.3 Absolute continuity 188
8.4 Herglotz functions 193
8.5 Loewner's differential equation 194
8.6 Solution of the nonlinear equation 198
8.7 Solution of Loewner's differential equation 204
Chapter 9
Coefficient Inequalities
9.1 Three famous problems 209
9.2 de Branges' method 214
9.3 Construction of the weight functions 219
9.4 Askey Gasper inequality 226
Notes 233
Errata to Hardy Classes and Operator Theory 236
Bibliography 237
Index 245 |
| any_adam_object | 1 |
| author | Rosenblum, Marvin Rovnyak, James |
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| discipline | Mathematik |
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| language | English |
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| spelling | Rosenblum, Marvin Verfasser aut Topics in Hardy classes and univalent functions Marvin Rosenblum, James Rovnyak Basel ; Boston, Mass. ; Berlin Birkhäuser Verlag 1994 IX, 250 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Birkhäuser Advanced Texts Literaturverzeichnis Seiten 237 - 244 Fonctions univalentes Fonctions univalentes ram Hardy, Classes de Hardy, classes de ram Hardy-ruimten gtt Univalente functies gtt classe Hardy inriac espace Hardy inriac fonction harmonique inriac fonction sous-harmonique inriac fonction univalente inriac théorie opérateur inriac Hardy classes Univalent functions Schlichte Funktion (DE-588)4131418-9 gnd rswk-swf Hardy-Klasse (DE-588)4159107-0 gnd rswk-swf Hardy-Klasse (DE-588)4159107-0 s DE-604 Schlichte Funktion (DE-588)4131418-9 s 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=006471646&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosenblum, Marvin Rovnyak, James Topics in Hardy classes and univalent functions Fonctions univalentes Fonctions univalentes ram Hardy, Classes de Hardy, classes de ram Hardy-ruimten gtt Univalente functies gtt classe Hardy inriac espace Hardy inriac fonction harmonique inriac fonction sous-harmonique inriac fonction univalente inriac théorie opérateur inriac Hardy classes Univalent functions Schlichte Funktion (DE-588)4131418-9 gnd Hardy-Klasse (DE-588)4159107-0 gnd |
| subject_GND | (DE-588)4131418-9 (DE-588)4159107-0 |
| title | Topics in Hardy classes and univalent functions |
| title_auth | Topics in Hardy classes and univalent functions |
| title_exact_search | Topics in Hardy classes and univalent functions |
| title_full | Topics in Hardy classes and univalent functions Marvin Rosenblum, James Rovnyak |
| title_fullStr | Topics in Hardy classes and univalent functions Marvin Rosenblum, James Rovnyak |
| title_full_unstemmed | Topics in Hardy classes and univalent functions Marvin Rosenblum, James Rovnyak |
| title_short | Topics in Hardy classes and univalent functions |
| title_sort | topics in hardy classes and univalent functions |
| topic | Fonctions univalentes Fonctions univalentes ram Hardy, Classes de Hardy, classes de ram Hardy-ruimten gtt Univalente functies gtt classe Hardy inriac espace Hardy inriac fonction harmonique inriac fonction sous-harmonique inriac fonction univalente inriac théorie opérateur inriac Hardy classes Univalent functions Schlichte Funktion (DE-588)4131418-9 gnd Hardy-Klasse (DE-588)4159107-0 gnd |
| topic_facet | Fonctions univalentes Hardy, Classes de Hardy, classes de Hardy-ruimten Univalente functies classe Hardy espace Hardy fonction harmonique fonction sous-harmonique fonction univalente théorie opérateur Hardy classes Univalent functions Schlichte Funktion Hardy-Klasse |
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