Abstract analytic function theory and Hardy algebras:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1977
|
| Schriftenreihe: | Lecture notes in mathematics
593 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 260 S. |
| ISBN: | 3540082522 0387082522 |
Internformat
MARC
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| 100 | 1 | |a Barbey, Klaus |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Abstract analytic function theory and Hardy algebras |c Klaus Barbey ; Heinz König |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1977 | |
| 300 | |a VII, 260 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 593 | |
| 650 | 7 | |a Algèbres de fonctions |2 ram | |
| 650 | 4 | |a Analyse fonctionnelle | |
| 650 | 4 | |a Fonctions analytiques | |
| 650 | 7 | |a Fonctions analytiques |2 ram | |
| 650 | 4 | |a Fonctions méromorphes | |
| 650 | 7 | |a Hardy, Espaces de |2 ram | |
| 650 | 4 | |a Mathématiques | |
| 650 | 7 | |a algèbre Banach |2 inriac | |
| 650 | 7 | |a algèbre Hardy |2 inriac | |
| 650 | 7 | |a fonction analytique |2 inriac | |
| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hardy-Algebra |0 (DE-588)4159106-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hardy-Algebra |0 (DE-588)4159106-9 |D s |
| 689 | 0 | 1 | |a Funktionentheorie |0 (DE-588)4018935-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a König, Heinz |e Verfasser |4 aut | |
| 830 | 0 | |a Lecture notes in mathematics |v 593 |w (DE-604)BV000676446 |9 593 | |
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Datensatz im Suchindex
| _version_ | 1804116699855716352 |
|---|---|
| adam_text | Contents
Chapter I. Boundary Value Theory for Harmonic and Holomorphic
Functions in the Unit Disk 1
1. Harmonic Functions 1
2. Pointwise Convergence: The Fatou Theorem and its Converse. . 6
3. Holomorphic Functions 12
4. The Function Classes Hoi*(D) and H* (D) 16
Notes 21
Chapter II. Function Algebras: The Bounded-Measurable Situation. . 22
1. Szego Functional and Fundamental Lemma 22
2. Measure Theory: Prebands and Bands 26
3. The abstract F.and M.Riesz Theorem 31
4. Gleason Parts 34
5. The abstract Szego-Kolmogorov-Krein Theorem 36
Notes 42
Chapter III. Function Algebras: The Compact-Continuous Situation . 44
1. Representative Measures and Jensen Measures 44
2. Return to the abstract F.and M.Riesz Theorem 47
3. The Gleason and Harnack Metrics 48
4. Comparison of the two Gleason Part Decompositions 54
Notes 58
Chapter IV. The Abstract Hardy Algebra Situation 59
1. Basic Notions and Connections with the Function
Algebra Situation 60
2. The Functional a 66
3. The Function Classes H* and L* 69
4. The Szego Situation 76
Notes 79
Chapter V. Elements of Abstract Hardy Algebra Theory 81
1. The Moduli of the invertible Elements of H 81
2. Substitution into entire Functions 84
VI
3. Substitution into Functions of Class Hoi (D) 85
4. The Function Class H+ 91
5. Weak-L Properties of the Functions in H 97
6. Value Carrier and Lumer Spectrum 102
Notes 106
Chapter VI. The Abstract Conjugation 108
1. A Representation Theorem 110
2. Definition of the abstract Conjugation 111
3. Characterization of E with the means of M 115
4. The basic Approximation Theorem 119
5. The Marcel Riesz and Kolmogorov Estimations 126
6. Special Situations 138
7. Return to the Marcel Riesz and Kolmogorov Estimations. ... 144
Notes 146
Chapter VII. Analytic Disks and Isomorphisms with the Unit
Disk Situation 149
1 . The Invariant Subspace Theorem 149
2. The Maximality Theorem 151
3. The Analytic Disk Theorem. . . .. , 155
4. The Isomorphism Theorem 160
5. Complements on the simple Invariance of H 165
6. A Class of Examples 167
Notes 170
Chapter VIII. Weak Compactness of M 172
1. The Decomposition Theorem of Hewitt-Yosida 172
2. Strict Convergence 175
3. Characterization Theorem and Main Result 177
Notes 180
Chapter IX. Logmodular Densities and Small Extensions 181
1. Logmodular Densities 181
2. The Closed Subgroup Lemma 186
3. Small Extensions 190
Notes 197
VII
Chapter X. Function Algebras on Compact Planar Sets 198
1. Consequences of the abstract Hardy Algebra Theory 199
2. The Cauchy Transformation of Measures 204
3. Basic Facts on P (K) = R (K) c A (K) 209
4. On the annihilating and the representing Measures
for R(K) and A(K) 214
5. On the Gleason Parts for R(K) and A(K) 218
6. The Logarithmic Transformation of Measures and the
Logarithmic Capacity of Planar Sets 221
7. The Walsh Theorem 227
8. Application to the Problem of Rational Approximation .... 231
Notes 234
Appendix 2 36
1. Linear Functionals and the Hahn-Banach Theorem 236
2. Measure Theory 2 39
3. The Cauchy Formula via the Divergence Theorem 241
Notes 244
References 245
Notation Index 255
Subject Index 257
|
| any_adam_object | 1 |
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| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)612110835 (DE-599)BVBBV002243940 |
| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV002243940 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:40Z |
| institution | BVB |
| isbn | 3540082522 0387082522 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001474675 |
| oclc_num | 612110835 |
| open_access_boolean | |
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| physical | VII, 260 S. |
| publishDate | 1977 |
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| publishDateSort | 1977 |
| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Barbey, Klaus Verfasser aut Abstract analytic function theory and Hardy algebras Klaus Barbey ; Heinz König Berlin [u.a.] Springer 1977 VII, 260 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 593 Algèbres de fonctions ram Analyse fonctionnelle Fonctions analytiques Fonctions analytiques ram Fonctions méromorphes Hardy, Espaces de ram Mathématiques algèbre Banach inriac algèbre Hardy inriac fonction analytique inriac Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Hardy-Algebra (DE-588)4159106-9 gnd rswk-swf Hardy-Algebra (DE-588)4159106-9 s Funktionentheorie (DE-588)4018935-1 s DE-604 König, Heinz Verfasser aut Lecture notes in mathematics 593 (DE-604)BV000676446 593 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001474675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barbey, Klaus König, Heinz Abstract analytic function theory and Hardy algebras Lecture notes in mathematics Algèbres de fonctions ram Analyse fonctionnelle Fonctions analytiques Fonctions analytiques ram Fonctions méromorphes Hardy, Espaces de ram Mathématiques algèbre Banach inriac algèbre Hardy inriac fonction analytique inriac Funktionentheorie (DE-588)4018935-1 gnd Hardy-Algebra (DE-588)4159106-9 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4159106-9 |
| title | Abstract analytic function theory and Hardy algebras |
| title_auth | Abstract analytic function theory and Hardy algebras |
| title_exact_search | Abstract analytic function theory and Hardy algebras |
| title_full | Abstract analytic function theory and Hardy algebras Klaus Barbey ; Heinz König |
| title_fullStr | Abstract analytic function theory and Hardy algebras Klaus Barbey ; Heinz König |
| title_full_unstemmed | Abstract analytic function theory and Hardy algebras Klaus Barbey ; Heinz König |
| title_short | Abstract analytic function theory and Hardy algebras |
| title_sort | abstract analytic function theory and hardy algebras |
| topic | Algèbres de fonctions ram Analyse fonctionnelle Fonctions analytiques Fonctions analytiques ram Fonctions méromorphes Hardy, Espaces de ram Mathématiques algèbre Banach inriac algèbre Hardy inriac fonction analytique inriac Funktionentheorie (DE-588)4018935-1 gnd Hardy-Algebra (DE-588)4159106-9 gnd |
| topic_facet | Algèbres de fonctions Analyse fonctionnelle Fonctions analytiques Fonctions méromorphes Hardy, Espaces de Mathématiques algèbre Banach algèbre Hardy fonction analytique Funktionentheorie Hardy-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001474675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT barbeyklaus abstractanalyticfunctiontheoryandhardyalgebras AT konigheinz abstractanalyticfunctiontheoryandhardyalgebras |