无限维空间上的复分析 [Complex Analysis on Infintie Dimensional Spaces] pdf epub mobi txt 电子书下载 2025

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出版社：世界图书出版公司

ISBN：9787510070310

版次：1

商品编码：11483419

包装：平装

外文名称：Complex Analysis on Infintie Dimensional Spaces

开本：24开

出版时间：2014-04-01

用纸：胶版纸

页数：543

正文语种：英文

具体描述

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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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