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多复变中的全纯函数和积分表示 英文PDF|Epub|txt|kindle电子书版本网盘下载
- （美）兰基著 著
- 出版社： 北京：世界图书北京出版公司
- ISBN：9787510044052
- 出版时间：2012
- 标注页数：391页
- 文件大小：74MB
- 文件页数：411页
- 主题词：全纯函数－英文；积分表示－英文
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图书目录
CHAPTER Ⅰ Elementary Local Properties of Holomorphic Functions1
1．Holomorphic Functions1
2．Holomorphic Maps18
3．Zero Sets of Holomorphic Functions31
Notes for ChapterⅠ40
CHAPTER Ⅱ Domains of Holomorphy and Pseudoconvexity42
1．Elementary Extension Phenomena43
2．Natural Boundaries and Pseudoconvexity48
3．The Convexity Theory of Cartan and Thullen67
4．Plurisubharmonic Functions82
5．Characterizations of Pseudoconvexity92
Notes for Chapter Ⅱ101
CHAPTER Ⅲ Differential Forms and Hermitian Geometry104
1．Calculus on Real Differentiable Manifolds105
2．Complex Structures122
3．Hermitian Geometry in Cn131
Notes for Chapter Ⅲ143
CHAPTER Ⅳ Integral Representations in Cn144
1．The Bochner-Martinelli-Koppelman Formula145
2．Some Applications159
3．The General Homotopy Formula168
4．The Bergman Kernel179
Notes for Chapter Ⅳ187
CHAPTER Ⅴ The Levi Problem and the Solution of ？ on Strictly Pseudoconvex Domains193
1．A Parametrix for ？ on Strictly Pseudoconvex Domains194
2．A Solution Operator for ？199
3．The Lipschitz 1/2-Estimate206
Notes for Chapter Ⅴ214
CHAPTER Ⅵ Function Theory on Domains of Holomorphy in Cn216
1．Approximation and Exhaustions217
2．？-Cohomological Characterization of Stein Domains227
3．Topological Properties of Stein Domains229
4．Meromorphic Functions and the Additive Cousin Problem232
5．Holomorphic Functions with Prescribed Zeroes239
6．Preview:Cohomology of Coherent Analytic Sheaves252
Notes for Chapter Ⅵ272
CHAPTER Ⅶ Topics in Function Theory on Strictly Pseudoconvex Domains275
1．A Cauchy Kernel for Strictly Pseudoconvex Domains276
2．Uniform Approximation on D282
3．The Kernel of Henkin and Ramirez285
4．Gleason's Problem and Decomposition in A(D)292
5．Lp Estimates for Sol utions of ？296
6．Approximation of Holomorphic Functions in Lp Norm305
7．Regularity Properties of the Bergman Projection309
8．Boundary Regularity of Biholomorphic Maps326
9．The Reflection Principle342
Notes for Chapter Ⅶ351
Appendix A358
Appendix B360
Appendix C362
Bibliography365
Glossary of Symbols and Notations376
Index381