简介
《无限维空间上的复分析》全面讲述了和局部凸空间中正则函数空间里的局部凸空间结够有关的许多问题。前三章引入多项式的基本性质和局部凸空间上的调和函数，紧接着的两章介绍了紧开拓扑、Nachbin拓扑和可数开覆盖产生的拓扑之间的关系。最后一章重新讲述了前面各章引进的无限维正则内在各种概念之间相互关系。完整的注解、历史背景、练习、附录和参考书目使得成为了无价之宝，然而书中来自各个领域学者的观点的表达和展示，能够吸引许多不同背景的数学人士。读者对象；数学专业的研究生、老师和相关的科研人员。
目录
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
无限维空间上的复分析
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