丁南編著的《無限維空間上的複分析》全面講述了和局部凸空間中正則函式空間裡的局部凸空間結夠有關的許多問題。前三章引入多項式的基本性質和局部凸空間上的調和函式，緊接著的兩章介紹了緊開拓撲、Nachbin拓撲和可數開覆蓋產生的拓撲之間的關係。最後一章重新講述了前面各章引進的無限維正則內在各種概念之間相互關係。完整的註解、歷史背景、練習、附錄和參考書目使得成為了無價之寶，然而書中來自各個領域學者的觀點的表達和展示，能夠吸引許多不同背景的數學人士。讀者對象；數學專業的研究生、老師和相關的科研人員。
基本介紹
- 書名：無限維空間上的複分析
- 作者：S.丁南 (Sean Dineen)
- 出版日期：2014年6月17日
- 開本：24
- 品牌：世界圖書出版公司北京公司
- 外文名：Complex Analysis on Infinite Dimensional Spaces
- 出版社：世界圖書出版公司
- 頁數：543頁
- ISBN：9787510070310
Chapter 1. Polynomials
1.1 Continuous Polynomials
1.2 Topologies on Spaces of Polynomials
1.3 Geometry of Spaces of Polynomials
1.4 Exercises
1.5 Notes
Chapter 2. Duality Theory for Polynomials
2.1 Special Spaces of Polynomials and the Approximation Property
2.2 Nuclear Spaces
2.3 Integral Polynomials and the Radon-Nikodym Property
2.4 Reflexivity and Related Concepts
2.5 Exercises
2.6 Notes
Chapter 3. Holomorphic Mappings between Locally Convex Spaces
3.1 Holomorphic Functions
3.2 Topologies on Spaces of Holomorphic Mappings
3.3 The Quasi-Local Theory of Holomorphic Functions
3.4 Polynomials in the Quasi-Local Theory
3.5 Exercises
3.6 Notes
Chapter 4. Decompositions of Holomorphic Functions
4.1 Decompositions of Spaces of Holomorphic Functions
4.2 Tω=Tδ for Frechet Spaces
4.3 Tb = Tω for Frechet Spaces
4.4 Examples and Counterexamples
4.5 Exercises
4.6 Notes
Chapter 5. Riemann Domains
5.1 Holomorphic Germs on a Frechet Space
5.2 Riemann Domains over Locally Convex Spaces
5.3 Exercises
5.4 Notes
Chapter 6. Holomorphic Extensions
6.1 Extensions from Dense Subspaces
6.2 Extensions from Closed Subspaces
6.3 Holomorphic Functions of Bounded Type
6.4 Exercises
6.5 Notes
Appendix. Remarks on Selected Exercises
References
Index
1.1 Continuous Polynomials
1.2 Topologies on Spaces of Polynomials
1.3 Geometry of Spaces of Polynomials
1.4 Exercises
1.5 Notes
Chapter 2. Duality Theory for Polynomials
2.1 Special Spaces of Polynomials and the Approximation Property
2.2 Nuclear Spaces
2.3 Integral Polynomials and the Radon-Nikodym Property
2.4 Reflexivity and Related Concepts
2.5 Exercises
2.6 Notes
Chapter 3. Holomorphic Mappings between Locally Convex Spaces
3.1 Holomorphic Functions
3.2 Topologies on Spaces of Holomorphic Mappings
3.3 The Quasi-Local Theory of Holomorphic Functions
3.4 Polynomials in the Quasi-Local Theory
3.5 Exercises
3.6 Notes
Chapter 4. Decompositions of Holomorphic Functions
4.1 Decompositions of Spaces of Holomorphic Functions
4.2 Tω=Tδ for Frechet Spaces
4.3 Tb = Tω for Frechet Spaces
4.4 Examples and Counterexamples
4.5 Exercises
4.6 Notes
Chapter 5. Riemann Domains
5.1 Holomorphic Germs on a Frechet Space
5.2 Riemann Domains over Locally Convex Spaces
5.3 Exercises
5.4 Notes
Chapter 6. Holomorphic Extensions
6.1 Extensions from Dense Subspaces
6.2 Extensions from Closed Subspaces
6.3 Holomorphic Functions of Bounded Type
6.4 Exercises
6.5 Notes
Appendix. Remarks on Selected Exercises
References
Index
