The Schwarz function and its generalization to higher dimensions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
John Wiley & Sons
1992
|
| Schriftenreihe: | University of Arkansas <Fayetteville, Ark.>: The University of Arkansas Lecture Notes in the Mathematical Sciences
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 108 S. |
| ISBN: | 047157127X |
Internformat
MARC
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| 245 | 1 | 0 | |a The Schwarz function and its generalization to higher dimensions |c Harold S. Shapiro, Mathematical Institute, Royal Institute of Technology, Stockholm, Sweden |
| 264 | 1 | |a New York, NY [u.a.] |b John Wiley & Sons |c 1992 | |
| 300 | |a XI, 108 S. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Preface ix
Chapter 1 The Schwarz principle of reflection 1
1.1 Introduction, 1
1.2 The Schwarz function, 2
1.3 Anti conformal reflection, 4
1.4 Schwarzian reflection, generalized, 5
1.5 The Schwarz potential, 7
Chapter 2 The logarithmic potential, balayage, and quadrature
domains 9
2.1 Analytic continuation of the potential, 9
2.2 Balayage, 11
2.3 Quadrature domains, 13
Chapter 3 Examples of quadrature identities 16
3.1 About the terminology, 16
3.2 Examples, 17
3.3 Examples, continued, 21
3.4 Examples of a q.d. with a singular boundary point, 22
3.5 An example of balayage inwards , 23
Chapter 4 Quadrature domains; basic properties, I 24
4.1 Notations, etc., 24
4.2 Quadrature domains and the Schwarz potential, 25
4.3 Some applications, 29
4.4 Subharmonic quadrature domains, 36
Chapter 5 Quadrature domains: basic properties, II 39
5.1 Regularity of the boundary, 39
5.2 Valency of the Schwarz function, 40
5.3 Variational properties of q.d., 41
5.4 Other varieties of quadrature domains, 44
5.5 Existence of q.d., 50
5.6 Conclusion, 51
vii
Chapter 6 Schwarzian reflection, revisited 52
6.1 Reformulation in terms of harmonic functions, 52
6.2 Study s interpretation of Schwarzian reflection, 55
6.3 Failure of Schwarzian reflection in R3, 60
Chapter 7 Projectors from L2(dG.) to ifii.dil) 63
7.1 Introduction, 63
7.2 The Hilbert operator of a plane domain, 63
7.3 Relation to the Neumann Poincart problem, 66
7.4 Proofs of the preceding theorems, 68
7.5 A property of the Szego projector S, 72
Chapter 8 The Friedrichs operator 74
8.1 Introduction, 74
8.2 The Friedrichs operator, 74
8.3 Weak* limits of sequences in L^ft), 76
8.4 The Friedrichs operator, geometry, and the Schwarz
function, 80
8.5 The Friedrichs operator and quadrature domains, 82
Chapter 9 Concluding remarks 84
9.1 The Schwarz potential in Cn, 84
9.2 The ellipse, revisited, 85
9.3 Propagation of singularities, an example, 87
9.4 The ellipse, concluded, 89
9.5 The sphere, revisited, 91
9.6 Further horizons, 92
9.7 Conclusion, 95
Bibliography 97
Index 105
viii
|
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| discipline | Mathematik |
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| id | DE-604.BV005462228 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:29:57Z |
| institution | BVB |
| isbn | 047157127X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003418808 |
| oclc_num | 246882552 |
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| physical | XI, 108 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | John Wiley & Sons |
| record_format | marc |
| series | University of Arkansas <Fayetteville, Ark.>: The University of Arkansas Lecture Notes in the Mathematical Sciences |
| series2 | University of Arkansas <Fayetteville, Ark.>: The University of Arkansas Lecture Notes in the Mathematical Sciences A Wiley-Interscience Publication |
| spelling | Shapiro, Harold S. 1928-2021 Verfasser (DE-588)130422924 aut The Schwarz function and its generalization to higher dimensions Harold S. Shapiro, Mathematical Institute, Royal Institute of Technology, Stockholm, Sweden New York, NY [u.a.] John Wiley & Sons 1992 XI, 108 S. txt rdacontent n rdamedia nc rdacarrier University of Arkansas <Fayetteville, Ark.>: The University of Arkansas Lecture Notes in the Mathematical Sciences 9 A Wiley-Interscience Publication Schwarzsche Funktion Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Schwarzsche Funktion (DE-588)4180363-2 gnd rswk-swf Schwarzsche Funktion (DE-588)4180363-2 s Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s DE-604 University of Arkansas <Fayetteville, Ark.>: The University of Arkansas Lecture Notes in the Mathematical Sciences 9 (DE-604)BV000007122 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003418808&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shapiro, Harold S. 1928-2021 The Schwarz function and its generalization to higher dimensions University of Arkansas <Fayetteville, Ark.>: The University of Arkansas Lecture Notes in the Mathematical Sciences Schwarzsche Funktion Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd Schwarzsche Funktion (DE-588)4180363-2 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4277015-4 (DE-588)4180363-2 |
| title | The Schwarz function and its generalization to higher dimensions |
| title_auth | The Schwarz function and its generalization to higher dimensions |
| title_exact_search | The Schwarz function and its generalization to higher dimensions |
| title_full | The Schwarz function and its generalization to higher dimensions Harold S. Shapiro, Mathematical Institute, Royal Institute of Technology, Stockholm, Sweden |
| title_fullStr | The Schwarz function and its generalization to higher dimensions Harold S. Shapiro, Mathematical Institute, Royal Institute of Technology, Stockholm, Sweden |
| title_full_unstemmed | The Schwarz function and its generalization to higher dimensions Harold S. Shapiro, Mathematical Institute, Royal Institute of Technology, Stockholm, Sweden |
| title_short | The Schwarz function and its generalization to higher dimensions |
| title_sort | the schwarz function and its generalization to higher dimensions |
| topic | Schwarzsche Funktion Funktionentheorie (DE-588)4018935-1 gnd Mehrere Variable (DE-588)4277015-4 gnd Schwarzsche Funktion (DE-588)4180363-2 gnd |
| topic_facet | Schwarzsche Funktion Funktionentheorie Mehrere Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003418808&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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