文件名称:无限维空间上的复分析(英文版)

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  • 2020-10-24
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无限维空间上的复分析(英文版) 出版时间:2014年版 内容简介   Infinite dimensional holomorphy is the study of holomorphic or analytic functions over complex topological vector spaces. The terms in this descr iption 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. 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
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