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内容简介

　　Infinite dimensional holomorphy is the study of holomorphic or analytic functions over complex topological vector spaces. The terms in this description are easily stated and explained and allow the subject to project itself initially， and innocently， as a compact theory with well defined boundaries. However， a comprehensive study would include delving into， and interacting with， not only the obvious topics of topology， several complex variables theory and functional analysis but also， differential geometry， Jordan algebras， Lie groups， operator theory， logic， differential equations and fixed point theory. This diversity leads to a dynamic synthesis of ideas and to an appreciation of a remarkable feature of mathematics - its unity. Unity requires synthesis while synthesis leads to unity.

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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
Chapter 5. Riemann Domains
Chapter 6. Holomorphic Extensions

前言/序言

无限维空间上的复分析 [Complex Analysis on Infintie Dimensional Spaces] 电子书 下载 mobi epub pdf txt

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无限维的复分析是个新鲜的事物。鉴于复分析在数学的重要性，数学工作者也肯定会重视无限维的理论，不过，在学校，好像很少听到提起。本书最早是斯普林格出版社出版的，世图影印。本书的一大特色是有历史注解，交待了很多背景，也有很多难度不同的练习，也有很详尽的参考书目，这些都是这本书最有价值的资料

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