無限維空間上的復分析 [Complex Analysis on Infintie Dimensional Spaces] 下載 mobi epub pdf 電子書 2025

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內容簡介

　　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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目錄

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

無限維空間上的復分析 [Complex Analysis on Infintie Dimensional Spaces] 下載 mobi epub pdf txt 電子書 格式

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無限維的復分析是個新鮮的事物。鑒於復分析在數學的重要性，數學工作者也肯定會重視無限維的理論，不過，在學校，好像很少聽到提起。本書最早是斯普林格齣版社齣版的，世圖影印。本書的一大特色是有曆史注解，交待瞭很多背景，也有很多難度不同的練習，也有很詳盡的參考書目，這些都是這本書最有價值的資料

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