Functional Analysis: Introduction to Further Topics in Analysis (Princeton Lectures in Analysis, No. 4) (Hardcover)

Elias M. Stein, Rami Shakarchi

  • 出版商: Princeton University
  • 出版日期: 2011-09-11
  • 售價: $1,580
  • 貴賓價: 9.8$1,548
  • 語言: 英文
  • 頁數: 448
  • 裝訂: Hardcover
  • ISBN: 0691113874
  • ISBN-13: 9780691113876
  • 立即出貨 (庫存=1)

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商品描述

This is the fourth and final volume in "The Princeton Lectures in Analysis", a series of textbooks that aim to present, in an integrated manner, the core areas of analysis. Beginning with the basic facts of functional analysis, this volume looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. The authors then use the Baire category theorem to illustrate several points, including the existence of Besicovitch sets. The second half of this book introduces readers to other central topics in analysis, such as probability theory and Brownian motion, which culminates in the solution of Dirichlet's problem. The concluding chapters explore several complex variables and oscillatory integrals in Fourier analysis, and illustrate applications to such diverse areas as nonlinear dispersion equations and the problem of counting lattice points. Throughout this book, the authors focus on key results in each area and stress the organic unity of the subject. This title offers a comprehensive and authoritative text that treats some of the main topics of modern analysis. It takes a look at basic functional analysis and its applications in harmonic analysis, probability theory, and several complex variables. It provides key results in each area that are discussed in relation to other areas of mathematics. It highlights the organic unity of large areas of analysis traditionally split into subfields. It provides interesting exercises and problems that illustrate ideas. Clear proofs provided.

商品描述(中文翻譯)

這是「普林斯頓分析講座」系列的第四冊,也是最後一冊,旨在以整合的方式呈現分析學的核心領域。本冊從泛函分析的基本事實開始,探討巴拿赫空間、Lp空間和分佈理論,並突出它們在調和分析中的作用。作者們利用貝爾類別定理來說明幾個重點,包括Besicovitch集合的存在性。本書的後半部分介紹讀者其他分析學的核心主題,如概率論和布朗運動,最終解決了狄利克雷問題。結尾章節探討了幾個複變數和傅立葉分析中的振盪積分,並展示了在非線性色散方程和格點計數問題等各個領域的應用。在整本書中,作者們專注於每個領域的關鍵結果,並強調了這個學科的有機統一性。本書提供了一個全面權威的文本,涵蓋了現代分析學的一些主要主題。它介紹了基本的泛函分析及其在調和分析、概率論和幾個複變數中的應用。它提供了每個領域的關鍵結果,並將其與其他數學領域相關聯。它突出了傳統上被分為子領域的大範圍分析學的有機統一性。它提供了有趣的練習和問題,以說明思想。提供清晰的證明。