内容简介

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 the 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 the book, the authors focus on key results in each area and stress the organic unity of the subject.

作品目录

Chapter 1 L^p spaces and Banach Spaces

Chapter 2 L^p spaces in Harmonic Analysis

Chapter 3 Distributions: Generalized Functions

Chapter 4 Applications of the Baire Category Theorem

Chapter 5 Rudiments of Probability Theory

Chapter 6 An Introduction to Brownian Motion

Chapter 7 A Glimpse into Several Complex Variables

Chapter 8 Oscillatory Integrals in Fourier Analysis