Functions of one complex variable II:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1996
|
| Ausgabe: | Corr. 2. pr. |
| Schriftenreihe: | Graduate texts in mathematics
159 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 394 S. |
| ISBN: | 0387944605 |
Internformat
MARC
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| 245 | 1 | 0 | |a Functions of one complex variable II |c John B. Conway |
| 250 | |a Corr. 2. pr. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a XVI, 394 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 159 | |
| 650 | 4 | |a Functions of complex variables | |
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| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804126241751564288 |
|---|---|
| adam_text | Contents
of
Volume
II
Preface vii
13
Return to Basics
1
1
Regions and Curves
..................... . 1
2
Derivatives and Other Recollections
............. 6
3
Harmonic Conjugates and Primitives
............. 14
4
Analytic Arcs and the Reflection Principle
.......... 16
5
Boundary Values for Bounded Analytic Functions
...... 21
14
Conformai
Equivalence for Simply Connected Regions
29
1
Elementary Properties and Examples
............. 29
2
Crosscuts
............................ 33
3
Prime Ends
........................... 40
4
Impressions of a Prime End
.................. 45
5
Boundary Values of Riemann Maps
.............. 48
6
The Area Theorem
....................... 56
7
Disk Mappings: The Class
S
.................. 61
15
Conformai
Equivalence for Finitely Connected Regions
71
1
Analysis on a Finitely Connected Region
........... 71
2
Conformai
Equivalence with an Analytic Jordan Region
. . 76
3
Boundary Values for
a Conformai
Equivalence Between Finitely
Connected Jordan Regions
................... 81
4
Convergence of
Univalent
Functions
............. 85
5
Conformai
Equivalence with a Circularly Slit Annulus
... 90
6
Conformai
Equivalence with a Circularly Slit Disk
..... 97
7
Conformai
Equivalence with a Circular Region
....... 100
16
Analytic Covering Maps
109
1
Results for Abstract Covering Spaces
............. 109
2
Analytic Covering Spaces
................... 113
3
The Modular Function
.................... . 116
4
Applications of the Modular Function
........... . 123
5
The Existence of the Universal Analytic Covering Map
. . . 125
17
De Branges s
Proof of the Bieberbach Conjecture
133
1
Subordination
.......................... 133
2
Loewner Chains
......................... 136
3
Loewner s Differential Equation
................ 142
4
The Milin Conjecture
..................... 148
5
Some Special Functions
.................... 156
6
The Proof of
de
Branges s Theorem
............. 160
18
Some Fundamental Concepts from Analysis
169
1
Bergman Spaces of Analytic and Harmonic Functions
. . . 169
2
Partitions of Unity
....................... 174
3
Convolution in Euclidean Space
................ 177
4
Distributions
.......................... 185
5
The Cauchy Transform
..................... 192
6
An Application: Rational Approximation
.......... 196
7
Fourier Series and
Cesàro
Sums
................ 198
19
Harmonic Functions Redux
205
1
Harmonic Functions on the Disk
............... 205
2
Fatou s Theorem
........................ 210
3
Semicontinuous Functions
................... 217
4
Subharmonic Functions
.................... 220
5
The Logarithmic Potential
................... 229
6
An Application: Approximation by Harmonic Functions
. . 235
7
The Dirichlet Problem
..................... 237
8
Harmonic
Majorants
...................... 245
9
The Green Function
...................... 246
10
Regular Points for the Dirichlet Problem
........... 253
11
The Dirichlet Principle and Sobolev Spaces
......... 259
20
Hardy Spaces on the Disk
269
1
Definitions and Elementary Properties
............ 269
2
The Nevanlinna Class
..................... 272
3
Factorization of Functions in the Nevanlinna Class
..... 278
4
The Disk Algebra
........................ 286
5
The Invariant Subspaces of Hp
................ 290
6
Szegö s
Theorem
........................ 295
21
Potential Theory in the Plane
301
1
Harmonic Measure
....................... 301
2
The Sweep of a Measure
.................... 311
3
The Robin Constant
...................... 313
4
The Green Potential
...................... 315
5
Polar Sets
............................ 320
6
More on Regular Points
.................... 328
7
Logarithmic Capacity: Part
1................. 331
8
Some Applications and Examples of Logarithmic Capacity
. 339
9
Removable Singularities for Functions in the Bergman Space
344
10
Logarithmic Capacity: Part
2................. 352
11
The
Transfinite
Diameter and Logarithmic Capacity
.... 355
12
The Refinement of a Subharmonic Function
......... 360
13
The Fine Topology
....................... 367
14
Wiener s criterion for Regular Points
............. 376
References
384
List of Symbols
389
Index
391
|
| any_adam_object | 1 |
| author | Conway, John B. 1939- |
| author_GND | (DE-588)110699882 |
| author_facet | Conway, John B. 1939- |
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| author_sort | Conway, John B. 1939- |
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| bvnumber | BV011704818 |
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| callnumber-label | QA331 |
| callnumber-raw | QA331.7 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 700 |
| classification_tum | MAT 300f |
| ctrlnum | (OCoLC)43536563 (DE-599)BVBBV011704818 |
| dewey-full | 515.93 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.93 |
| dewey-search | 515.93 |
| dewey-sort | 3515.93 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Corr. 2. pr. |
| format | Book |
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| id | DE-604.BV011704818 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:14:20Z |
| institution | BVB |
| isbn | 0387944605 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007892481 |
| oclc_num | 43536563 |
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| owner_facet | DE-91 DE-BY-TUM DE-29T DE-19 DE-BY-UBM DE-739 DE-703 DE-83 |
| physical | XVI, 394 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Conway, John B. 1939- Verfasser (DE-588)110699882 aut Functions of one complex variable II John B. Conway Corr. 2. pr. New York [u.a.] Springer 1996 XVI, 394 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 159 Functions of complex variables Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 Komplexe Variable (DE-588)4164905-9 s 1\p DE-604 Graduate texts in mathematics 159 (DE-604)BV000000067 159 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007892481&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 | Conway, John B. 1939- Functions of one complex variable II Graduate texts in mathematics Functions of complex variables Komplexe Variable (DE-588)4164905-9 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4164905-9 (DE-588)4018935-1 |
| title | Functions of one complex variable II |
| title_auth | Functions of one complex variable II |
| title_exact_search | Functions of one complex variable II |
| title_full | Functions of one complex variable II John B. Conway |
| title_fullStr | Functions of one complex variable II John B. Conway |
| title_full_unstemmed | Functions of one complex variable II John B. Conway |
| title_short | Functions of one complex variable II |
| title_sort | functions of one complex variable ii |
| topic | Functions of complex variables Komplexe Variable (DE-588)4164905-9 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Functions of complex variables Komplexe Variable Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007892481&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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