Holomorphic function theory in several variables: an introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
London
Springer [u.a.]
2011
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| Series: | Universitext
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 252 Seiten |
| ISBN: | 9780857290298 0857290290 9782759800834 2759800830 |
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| 240 | 1 | 0 | |a Théorie des fonctions holomorphes de plusiers variables |
| 245 | 1 | 0 | |a Holomorphic function theory in several variables |b an introduction |c Christine Laurent-Thiébaut |
| 264 | 1 | |a London |b Springer [u.a.] |c 2011 | |
| 300 | |a XIII, 252 Seiten | ||
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| adam_text | Titel: Holomorphic function theory in several variables
Autor: Laurent-Thiébaut, Christine
Jahr: 2011
Contents
Preface........................................................ IX
Introduction................................................... XI
I Elementary local properties of holomorphic functions of
several complex variables................................. 1
1 Notation and definitions................................. 1
2 The Cauchy formula for polydiscs........................ 3
3 The open mapping theorem.............................. 8
4 Series of holomorphic functions........................... 10
5 Holomorphic maps...................................... 11
6 Some holomorphic extension theorems .................... 13
II Currents and complex structures......................... 21
1 Currents .............................................. 21
2 Régularisation......................................... 28
3 Kronecker index of two currents.......................... 38
4 Complex analytic manifolds.............................. 44
5 Complex structures..................................... 46
6 Differential forms of type (p, q)........................... 48
7 The d operator and Dolbeault cohomology................. 49
8 Complex tangent space to the boundary of a domain........ 52
III The Bochner—Martinelli—Koppelman kernel and formula
and applications.......................................... 57
1 The Bochner-Martinelli-Koppelman kernel and formula..... 57
2 Existence of solutions to the d equation for compactly
supported data......................................... 63
3 Regularity of d......................................... 68
4 Hartogs phenomenon................................... 71
VI Contents
IV Extensions of CR functions............................... 75
1 The Bochner-Martinelli transform........................ 75
2 CR functions on a real hypersurface ...................... 79
3 Bochner s theorem...................................... 82
4 Stokes formula for CR functions......................... 86
5 Integral of the Bochner-Martinelli kernel.................. 88
6 An extension theorem for CR functions ................... 90
V Extensions of holomorphic and CR functions on manifolds 95
1 Cohomology with compact support and Hartogs phenomenon 95
2 Extension of C°° CR functions........................... 98
3 The Cauchy-Fantappié formula and Dolbeault s lemma.....100
4 The Dolbeault isomorphism..............................105
5 Bochner s theorem and extensions of CR functions on
manifolds..............................................110
VI Domains of holomorphy and pseudoconvexity.............113
1 Domains of holomorphy and holomorphic convexity.........113
2 Plurisubharmonic functions..............................121
3 Pseudoconvexity .......................................133
VII The Levi problem and the resolution of d in strictly
pseudoconvex domains....................................147
1 Solving d with Holder estimates in strictly convex open sets . 147
2 Local uniform approximation of 9-closed forms in strictly
pseudoconvex domains..................................157
3 Finiteness of Dolbeault cohomology groups of strictly
pseudoconvex domains..................................160
4 Invariance of Dolbeault cohomology under strictly
pseudoconvex extensions ................................162
5 Vanishing theorems for Dolbeault cohomology of strictly
pseudoconvex domains in Cn.............................166
6 Integral formulae for solving d with Holder estimates in
strictly pseudoconvex domains...........................168
7 The Levi problem in Cn.................................176
8 The Levi problem for complex analytic manifolds...........179
VIII Characterisation of removable singularities of CR
functions on a strictly pseudoconvex boundary ...........195
1 Reduction to continuous functions........................195
2 The two-dimensional case................................196
3 A cohomological characterisation in dimension ? ^ 3........198
4 Characterisation of weakly removable singularities..........200
Contents VII
Appendix
A Differentiable manifolds and differential forms............213
1 Differentiable manifolds.................................213
2 Partitions of unity......................................215
3 Cotangent space at a point and differential forms of degree 1. 216
4 The tangent space at a point and vector fields..............218
5 The algebra of differential forms..........................221
6 Integration of differential forms...........................226
7 Stokes theorem........................................230
 Sheaf theory..............................................233
C Functional analysis.......................................241
References.....................................................245
Index of notation..............................................249
Index..........................................................251
|
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| isbn | 9780857290298 0857290290 9782759800834 2759800830 |
| language | English French |
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| physical | XIII, 252 Seiten |
| publishDate | 2011 |
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| spelling | Laurent-Thiébaut, Christine Verfasser (DE-588)140204687 aut Théorie des fonctions holomorphes de plusiers variables Holomorphic function theory in several variables an introduction Christine Laurent-Thiébaut London Springer [u.a.] 2011 XIII, 252 Seiten txt rdacontent n rdamedia nc rdacarrier Universitext Includes bibliographical references and index Translated from the original french, published by EDP Sciences, CNRS Editions, 1997. Holomorphic functions Functions of several complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Funktionentheorie (DE-588)4018935-1 s Mehrere komplexe Variable (DE-588)4169285-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024154198&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Laurent-Thiébaut, Christine Holomorphic function theory in several variables an introduction Holomorphic functions Functions of several complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4169285-8 (DE-588)4018935-1 (DE-588)4123623-3 |
| title | Holomorphic function theory in several variables an introduction |
| title_alt | Théorie des fonctions holomorphes de plusiers variables |
| title_auth | Holomorphic function theory in several variables an introduction |
| title_exact_search | Holomorphic function theory in several variables an introduction |
| title_full | Holomorphic function theory in several variables an introduction Christine Laurent-Thiébaut |
| title_fullStr | Holomorphic function theory in several variables an introduction Christine Laurent-Thiébaut |
| title_full_unstemmed | Holomorphic function theory in several variables an introduction Christine Laurent-Thiébaut |
| title_short | Holomorphic function theory in several variables |
| title_sort | holomorphic function theory in several variables an introduction |
| title_sub | an introduction |
| topic | Holomorphic functions Functions of several complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Holomorphic functions Functions of several complex variables Mehrere komplexe Variable Funktionentheorie Lehrbuch |
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