Partial differential equations in several complex variables:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc. [u.a.]
2001
|
| Schriftenreihe: | AMS, IP studies in advanced mathematics
19 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 380 S. |
| ISBN: | 0821810626 |
Internformat
MARC
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| 100 | 1 | |a Chen, So-chin |d 1956- |e Verfasser |0 (DE-588)1056125012 |4 aut | |
| 245 | 1 | 0 | |a Partial differential equations in several complex variables |c So-Chin Chen ; Mei-Chi Shaw |
| 264 | 1 | |a Providence, RI |b American Math. Soc. [u.a.] |c 2001 | |
| 300 | |a XII, 380 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a AMS, IP studies in advanced mathematics |v 19 | |
| 650 | 7 | |a Differentiaaloperatoren |2 gtt | |
| 650 | 4 | |a Fonctions de plusieurs variables complexes | |
| 650 | 7 | |a Fonctions de plusieurs variables complexes |2 ram | |
| 650 | 7 | |a Partiële differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 7 | |a Équations aux dérivées partielles |2 ram | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Functions of several complex variables | |
| 650 | 0 | 7 | |a Mehrere komplexe Variable |0 (DE-588)4169285-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
| 689 | 0 | 1 | |a Mehrere komplexe Variable |0 (DE-588)4169285-8 |D s |
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| 700 | 1 | |a Shaw, Mei-Chi |d 1955- |e Verfasser |0 (DE-588)173488374 |4 aut | |
| 830 | 0 | |a AMS, IP studies in advanced mathematics |v 19 |w (DE-604)BV011103148 |9 19 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009045171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009045171 | ||
Datensatz im Suchindex
| _version_ | 1804128033629536257 |
|---|---|
| adam_text | Contents
Page
Preface xi
Chapter 1 Real and Complex Manifolds 1
1.1 Holomorphic Functions in Complex Euclidean Spaces 1
1.2 Real and Complex Manifolds 3
1.3 Tangent Spaces and the Hermitian Metric 5
1.4 Vector Bundles 6
1.5 Exterior Derivatives and the Cauchy Riemann Complex 8
1.6 The Frobenius Theorem 10
1.7 Inequivalence between the Ball and the Polydisc in C 13
Notes 14
Chapter 2 The Cauchy Integral Formula and its Applications 15
2.1 The Cauchy Integral Formula 15
2.2 The Bochner Martinelli Formula 22
2.3 The Cauchy Riemann Operator in C 25
Notes 33
Chapter 3 Holomorphic Extension and Pseudoconvexity 35
3.1 The Hartogs Extension Theorem 36
3.2 The Holomorphic Extension Theorem from a Compact
Hypersurface 39
3.3 A Local Extension Theorem 42
3.4 Pseudoconvexity 44
3.5 Domains of Holomorphy 52
3.6 The Levi Problem and the d Equation 56
Notes 57
vii
viii CONTENTS
Chapter 4 L2 Theory for d on Pseudoconvex Domains 59
4.1 Unbounded Operators in Hilbert Spaces 59
4.2 The 9 Neumann Problem 61
4.3 L2 Existence Theorems for d in Pseudoconvex Domains 67
4.4 L2 Existence Theorems for the 9 Neumann Operator 78
4.5 Pseudoconvexity and the Levi Problem 83
Notes 85
Chapter 5 The 9 Neumann Problem on Strongly
Pseudoconvex Manifolds 87
5.1 Subelliptic Estimates for the 9 Neumann Operator 88
5.2 Boundary Regularity for N and d*N 92
5.3 Function Theory on Manifolds 104
5.4 Almost Complex Structures 115
Notes 119
Chapter 6 Boundary Regularity for d on Pseudoconvex
Domains 121
6.1 Global Regularity for d on Pseudoconvex Domains with
Smooth Boundaries 122
6.2 Sobolev Estimates for the d Neumann Operator 128
6.3 The Bergman Projection and Boundary Regularity of
Biholomorphic Maps 139
6.4 Worm Domains 151
6.5 Irregularity of the Bergman Projection on Worm Domains 154
Notes 162
Chapter 7 Cauchy Riemann Manifolds and the
Tangential Cauchy Riemann Complex 165
7.1 CR Manifolds 165
7.2 The Tangential Cauchy Riemann Complex 167
7.3 Lewy s Equation 171
7.4 Linear Partial Differential Operators with Constant
Coefficients 173
Notes 175
Chapter 8 Subelliptic Estimates for Second Order
Differential Equations and Ob 177
8.1 Pseudodifferential Operators 177
CONTENTS ix
8.2 Hypoellipticity of Sum of Squares of Vector Fields 181
8.3 Subelliptic Estimates for the Tangential Cauchy Riemann
Complex 190
8.4 Local Regularity and the Hodge Theorem for ? , 196
Notes 203
Chapter 9 The Tangential Cauchy Riemann Complex
on Pseudoconvex CR Manifolds 207
9.1 The L2 Cauchy Problem for d 207
9.2 5 Closed Extensions of Forms and Cx Solvability of db 211
9.3 L2 Existence Theorems and Sobolev Estimates for db 217
9.4 The Hodge Decomposition Theorem for db 229
Notes 232
Chapter 10 Fundamental Solutions for Db on the
Heisenberg Group 235
10.1 Fundamental Solutions for ?;, on the Heisenberg Group 235
10.2 The Cauchy Szego Kernel on the Heisenberg Group 247
10.3 Local Solvability of the Lewy Operator 256
Notes 259
Chapter 11 Integral Representations for d and db 261
11.1 Integral Kernels in Several Complex Variables 262
11.2 The Homotopy Formula for d on Convex Domains 270
11.3 Homotopy Formulas for db on Strictly Convex Boundaries 277
11.4 Solvability for db on CR Manifolds with Boundaries 289
11.5 Lv Estimates for Local Solutions of db 297
11.6 The db Neumann Problem 308
Notes 311
Chapter 12 Embeddability of Abstract CR Structures 315
12.1 Introduction 315
12.2 Boutet de Monvel s Global Embeddability Theorem 317
12.3 Spherical Harmonics 320
12.4 Rossi s Global Nonembeddability Example 323
12.5 Nirenberg s Local Nonembeddability Example 326
Notes 334
x CONTENTS
Appendix 337
A. Sobolev Spaces 337
B. Interpolation Theorems and some Inequalities 341
C. Hardy Littlewood Lemma and its Variations 345
D. Friedrichs Lemma 350
Bibliography 353
Table of Notation 367
Index 373
|
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| author | Chen, So-chin 1956- Shaw, Mei-Chi 1955- |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| id | DE-604.BV013267488 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:42:49Z |
| institution | BVB |
| isbn | 0821810626 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009045171 |
| oclc_num | 45122750 |
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| physical | XII, 380 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | American Math. Soc. [u.a.] |
| record_format | marc |
| series | AMS, IP studies in advanced mathematics |
| series2 | AMS, IP studies in advanced mathematics |
| spelling | Chen, So-chin 1956- Verfasser (DE-588)1056125012 aut Partial differential equations in several complex variables So-Chin Chen ; Mei-Chi Shaw Providence, RI American Math. Soc. [u.a.] 2001 XII, 380 S. txt rdacontent n rdamedia nc rdacarrier AMS, IP studies in advanced mathematics 19 Differentiaaloperatoren gtt Fonctions de plusieurs variables complexes Fonctions de plusieurs variables complexes ram Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Équations aux dérivées partielles ram Differential equations, Partial Functions of several complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Mehrere komplexe Variable (DE-588)4169285-8 s DE-604 Shaw, Mei-Chi 1955- Verfasser (DE-588)173488374 aut AMS, IP studies in advanced mathematics 19 (DE-604)BV011103148 19 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009045171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chen, So-chin 1956- Shaw, Mei-Chi 1955- Partial differential equations in several complex variables AMS, IP studies in advanced mathematics Differentiaaloperatoren gtt Fonctions de plusieurs variables complexes Fonctions de plusieurs variables complexes ram Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Équations aux dérivées partielles ram Differential equations, Partial Functions of several complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4169285-8 (DE-588)4044779-0 |
| title | Partial differential equations in several complex variables |
| title_auth | Partial differential equations in several complex variables |
| title_exact_search | Partial differential equations in several complex variables |
| title_full | Partial differential equations in several complex variables So-Chin Chen ; Mei-Chi Shaw |
| title_fullStr | Partial differential equations in several complex variables So-Chin Chen ; Mei-Chi Shaw |
| title_full_unstemmed | Partial differential equations in several complex variables So-Chin Chen ; Mei-Chi Shaw |
| title_short | Partial differential equations in several complex variables |
| title_sort | partial differential equations in several complex variables |
| topic | Differentiaaloperatoren gtt Fonctions de plusieurs variables complexes Fonctions de plusieurs variables complexes ram Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Équations aux dérivées partielles ram Differential equations, Partial Functions of several complex variables Mehrere komplexe Variable (DE-588)4169285-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Differentiaaloperatoren Fonctions de plusieurs variables complexes Partiële differentiaalvergelijkingen Équations aux dérivées partielles Differential equations, Partial Functions of several complex variables Mehrere komplexe Variable Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009045171&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011103148 |
| work_keys_str_mv | AT chensochin partialdifferentialequationsinseveralcomplexvariables AT shawmeichi partialdifferentialequationsinseveralcomplexvariables |