Real analysis
著者
書誌事項
Real analysis
（A comprehensive course in analysis, pt. 1）
American Mathematical Society, c2015
大学図書館所蔵 件 / 全30件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
A Comprehensive Course in Analysis by Poincare Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis.
Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Frechet spaces, Schwartz space, and $L^p$ spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.
目次
Preliminaries
Topological spaces
A first look at Hilbert spaces and Fourier series
Measure theory
Convexity and Banach spaces
Tempered distributions and the Fourier transform
Bonus chapter: Probability basics
Bonus chapter: Hausdorff measure and dimension
Bonus chapter: Inductive limits and ordinary distributions
Bibliography
Symbol index
Subject index
Author index
Index of capsule biographies
「Nielsen BookData」 より
