Potential theory in the complex plane:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Edition: | 1. publ., transferred to digital print. |
| Series: | London Mathematical Society student texts
28 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 232 S. |
| ISBN: | 9780521461207 9780521466547 0521461200 |
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MARC
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| 100 | 1 | |a Ransford, Thomas |d 1958- |e Verfasser |0 (DE-588)143777912 |4 aut | |
| 245 | 1 | 0 | |a Potential theory in the complex plane |c Thomas Ransford |
| 250 | |a 1. publ., transferred to digital print. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a X, 232 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a London Mathematical Society student texts |v 28 | |
| 650 | 4 | |a Functions (Mathematics) | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 4 | |a Potential theory (Mathematics) | |
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Record in the Search Index
| _version_ | 1804141184512163840 |
|---|---|
| adam_text | Contents
Preface
ix
A Word about Notation
1
1
Harmonic Functions
3
1.1
Harmonic and Holomorphic Functions
............ 3
1.2
The Dirichlet Problem on the Disc
.............. 7
1.3
Positive Harmonic Functions
................. 13
Notes on Chapter
1.......................... 22
2
Subharmonic Functions
25
2.1
Upper Semicontinuous Functions
............... 25
2.2
Subharmonic Functions
.................... 27
2.3
The Maximum Principle
.................... 29
2.4
Criteria for Subharmonicity
.................. 35
2.5
Integrability
........................... 39
2.6
Convexity
............................ 43
2.7
Smoothing
............................ 48
Notes on Chapter
2 .......................... 51
3
Potential Theory
53
3.1
Potentials
............................ 53
3.2
Polar Sets
............................ 55
3.3
Equilibrium Measures
..................... 58
3.4
Upper Semicontinuous
Regularizaron
............ 62
3.5
Minus-Infinity Sets
....................... 65
3.6
Removable Singularities
.................... 67
3.7
The Generalized Laplacian
................... 71
3.8
Thinness
............................. 78
Notes on Chapter
3 .......................... 82
4
The Dirichlet Problem
85
4.1
Solution of the Dirichlet Problem
............... 85
4.2
Criteria for Regularity
..................... 91
4.3
Harmonic Measure
....................... 96
4.4
Green s Functions
....................... 106
4.5
The Poisson-Jensen Formula
................. 116
Notes on Chapter
4.......................... 126
5
Capacity
127
5.1
Capacity as a Set Function
.................. 127
5.2
Computation of Capacity
................... 132
5.3
Estimation of Capacity
..................... 137
5.4
Criteria for Thinness
...................... 146
5.5
Transfinite
Diameter
...................... 152
Notes on Chapter
5.......................... 160
6
Applications
161
6.1
Interpolation of LP-spaces
................... 161
6.2
Homogeneous Polynomials
................... 166
6.3
Uniform Approximation
.................... 169
6.4
Banach Algebras
........................ 176
6.5
Complex Dynamics
....................... 190
Notes on Chapter
6.......................... 206
A Borei
Measures
209
A.I Supports
............................. 209
A.2 Regularity
............................ 210
A.3 Radon Measures
........................ 211
A.
4
Weak*-Convergence
...................... 216
Bibliography
219
Index
225
Glossary of Notation
231
|
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| author | Ransford, Thomas 1958- |
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| classification_tum | MAT 310f |
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| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ., transferred to digital print. |
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| id | DE-604.BV036109696 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:11:50Z |
| institution | BVB |
| isbn | 9780521461207 9780521466547 0521461200 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018999903 |
| oclc_num | 316114601 |
| open_access_boolean | |
| owner | DE-739 |
| owner_facet | DE-739 |
| physical | X, 232 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society student texts |
| series2 | London Mathematical Society student texts |
| spelling | Ransford, Thomas 1958- Verfasser (DE-588)143777912 aut Potential theory in the complex plane Thomas Ransford 1. publ., transferred to digital print. Cambridge [u.a.] Cambridge Univ. Press 2008 X, 232 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 28 Functions (Mathematics) Functions of complex variables Potential theory (Mathematics) Komplexe Ebene (DE-588)4481425-2 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Potenzialtheorie (DE-588)4046939-6 s Komplexe Ebene (DE-588)4481425-2 s DE-604 London Mathematical Society student texts 28 (DE-604)BV000841726 28 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018999903&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ransford, Thomas 1958- Potential theory in the complex plane London Mathematical Society student texts Functions (Mathematics) Functions of complex variables Potential theory (Mathematics) Komplexe Ebene (DE-588)4481425-2 gnd Potenzialtheorie (DE-588)4046939-6 gnd |
| subject_GND | (DE-588)4481425-2 (DE-588)4046939-6 |
| title | Potential theory in the complex plane |
| title_auth | Potential theory in the complex plane |
| title_exact_search | Potential theory in the complex plane |
| title_full | Potential theory in the complex plane Thomas Ransford |
| title_fullStr | Potential theory in the complex plane Thomas Ransford |
| title_full_unstemmed | Potential theory in the complex plane Thomas Ransford |
| title_short | Potential theory in the complex plane |
| title_sort | potential theory in the complex plane |
| topic | Functions (Mathematics) Functions of complex variables Potential theory (Mathematics) Komplexe Ebene (DE-588)4481425-2 gnd Potenzialtheorie (DE-588)4046939-6 gnd |
| topic_facet | Functions (Mathematics) Functions of complex variables Potential theory (Mathematics) Komplexe Ebene Potenzialtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018999903&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000841726 |
| work_keys_str_mv | AT ransfordthomas potentialtheoryinthecomplexplane |