Harmonic approximation:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1995
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society: London Mathematical Society lecture note series
221 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 132 S. graph. Darst. |
| ISBN: | 052149799X |
Staff View
MARC
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| 100 | 1 | |a Gardiner, Stephen J. |d 1958- |e Verfasser |0 (DE-588)122123360 |4 aut | |
| 245 | 1 | 0 | |a Harmonic approximation |c Stephen J. Gardiner |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1995 | |
| 300 | |a XIII, 132 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society: London Mathematical Society lecture note series |v 221 | |
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| 650 | 0 | 7 | |a Approximation |0 (DE-588)4002498-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804124736866746368 |
|---|---|
| adam_text | Table
of
Contents
Preface
................................................. xi
0.
Review of thin sets
0.1
Introduction
........................................ 1
0.2
The fine topology
.................................... 2
0.3
Reduced functions and thinness
....................... 4
0.4
Thin sets and the Dirichlet problem
.................... 4
0.5
Wiener s criterion
.................................... 6
1.
Approximation on compact sets
1.1
Introduction
........................................ 7
1.2
Local approximation on compact sets with empty interior
. 8
1.3
Local harmonic approximation
........................ 11
1.4
Proof that (b) implies (a) in Theorem
1.3 ............... 14
1.5
Proof that (a) implies (b) in Theorem
1.3 ............... 15
1.6
Pole pushing
........................................ 16
1.7 Runge
approximation
................................ 18
1.8
Proof that (b) implies (a) in Theorem
1.10 ...___....... 20
1.9
Proof that (a) implies (b) in Theorem
1.10.............. 22
1.10
An analogue of Mergelyan s Theorem
.................. 23
1.11
The case where
η
= 2................................ 24
2.
Fusion of harmonic functions
2.1
Introduction
........................................ 27
2.2
Preliminary lemmas
.................................. 28
2.3
A fusion result
...................................... 32
3.
Approximation on relatively closed sets
3.1
Introduction
........................................ 39
3.2
Local connectedness
.................................. 40
3.3
Pole pushing
........................................ 42
3.4
A sufficient condition for
Runge
approximation
.......... 43
3.5
Relating the error to the set
E
........................ 45
3.6
Proof of Theorem
3.11 ............................... 48
3.7
A necessary condition for
Runge
approximation
......... 49
3.8 Runge
approximation
................................ 51
3.9
Approximation by functions in
Ћ(Е)
................... 55
3.10
Arakelyan approximation
............................. 57
3.11
Weak approximation
................................. 58
4.
Carleman
approximation
4.1
Introduction
........................................ 63
4.2
Decay of harmonic functions
.......................... 64
4.3
Approximation by functions in
7ί(Ε)
................... 65
4.4
Carleman
approximation
............................. 68
4.5
Approximation of functions in %{E)
................... 68
5.
Tangential approximation at infinity
5.1
Introduction
........................................ 73
5.2
Preliminary lemmas
.................................. 73
5.3
A fusion result
...................................... 78
5.4
Pole pushing
........................................ 80
5.5
Approximation of functions in
Ή.(Ε)
................... 81
5.6
Approximation of functions in C(E)
П
ЩЕ°)
........... 83
6.
Superharmonic extension and approximation
6.1
Introduction
........................................ 85
6.2
Strong extension
..................................... 85
6.3
Extension from compact sets
.......................... 88
6.4
Extension from relatively closed sets
................... 92
6.5 Runge
approximation
................................ 96
6.6
Approximation on compact sets
....................... 97
6.7
Approximation of functions in C(E)
Π
S(E°)
............ 99
7.
The Dirichlet problem with non-compact boundary
7.1
Introduction
........................................ 103
7.2
The Dirichlet problem
................................ 104
7.3
Proof that (b) implies (a) in Theorem
7.1 ............... 104
7.4
Proof that (a) implies (b) in Theorem
7.1 ............... 107
7.5
A maximum principle
................................ 108
8.
Further applications
8.1
Non-uniqueness for the Radon transform
............... 113
8.2
A universal harmonic function
......................... 116
8.3
Boundary cluster sets of subharmonic functions
.......... 117
8.4
Growth of harmonic functions along rays
............... 122
References
................................................ . 125
Index
..................................................___ 131
|
| any_adam_object | 1 |
| author | Gardiner, Stephen J. 1958- |
| author_GND | (DE-588)122123360 |
| author_facet | Gardiner, Stephen J. 1958- |
| author_role | aut |
| author_sort | Gardiner, Stephen J. 1958- |
| author_variant | s j g sj sjg |
| building | Verbundindex |
| bvnumber | BV010317555 |
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| dewey-full | 515.785 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.785 |
| dewey-search | 515.785 |
| dewey-sort | 3515.785 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV010317555 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:50:25Z |
| institution | BVB |
| isbn | 052149799X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006865513 |
| oclc_num | 246644256 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-634 DE-11 DE-188 DE-739 |
| owner_facet | DE-12 DE-384 DE-703 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-634 DE-11 DE-188 DE-739 |
| physical | XIII, 132 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society lecture note series |
| series2 | London Mathematical Society: London Mathematical Society lecture note series |
| spelling | Gardiner, Stephen J. 1958- Verfasser (DE-588)122123360 aut Harmonic approximation Stephen J. Gardiner 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1995 XIII, 132 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society lecture note series 221 Harmonische Funktion (DE-588)4159122-7 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf Harmonische Funktion (DE-588)4159122-7 s Approximation (DE-588)4002498-2 s DE-604 London Mathematical Society: London Mathematical Society lecture note series 221 (DE-604)BV000000130 221 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006865513&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gardiner, Stephen J. 1958- Harmonic approximation London Mathematical Society: London Mathematical Society lecture note series Harmonische Funktion (DE-588)4159122-7 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4159122-7 (DE-588)4002498-2 |
| title | Harmonic approximation |
| title_auth | Harmonic approximation |
| title_exact_search | Harmonic approximation |
| title_full | Harmonic approximation Stephen J. Gardiner |
| title_fullStr | Harmonic approximation Stephen J. Gardiner |
| title_full_unstemmed | Harmonic approximation Stephen J. Gardiner |
| title_short | Harmonic approximation |
| title_sort | harmonic approximation |
| topic | Harmonische Funktion (DE-588)4159122-7 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Harmonische Funktion Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006865513&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT gardinerstephenj harmonicapproximation |