Anthony W.Knapp的高级实分析

English | PDF | 2005 | 483 Pages | ISBN : 0817643826 | 3 MB

Advanced Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Basic Real Analysis (available separately or together as a Set), these works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Advanced Real Analysis requires of the reader a first course in measure theory, including an introduction to the Fourier transform and to Hilbert and Banach spaces. Some familiarity with complex analysis is helpful for certain chapters. The book is suitable as a text in graduate courses such as Fourier and functional analysis, modern analysis, and partial differential equations. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and forself-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician.

中文| PDF | 2005 | 483页| ISBN:0817643826| 3 MB高级实分析系统地开发了实分析中对每个数学家都至关重要的概念和工具，无论是纯粹的还是应用的，有抱负的还是成熟的。这些作品与配套的《基础真实分析》（单独或作为一套提供）一起，从全局的角度对这一主题进行了全面的论述，强调了真实分析与数学其他分支之间的联系。高级实分析要求读者学习测量理论的第一门课程，包括傅里叶变换、希尔伯特和巴拿赫空间的介绍。对复杂分析的一些熟悉对某些章节是有帮助的。这本书适合作为傅里叶和泛函分析、现代分析和偏微分方程等研究生课程的教材。因为这本书关注的是每个年轻数学家需要了解的关于真实分析的知识，所以无论是作为课程文本还是自学，尤其是对于准备资格考试的研究生来说，这本书都是理想的。它的范围和方法将吸引几乎所有纯数学领域的教师和教授，以及在统计学、数学物理和微分方程等分析领域工作的应用数学家。事实上，高级实分析的清晰度和广度使其成为每个数学家个人库中受欢迎的补充。

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