Fourier Integrals in Classical Analysis 经典分析中的傅立叶积分剑桥数学丛书系列精装

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作者Christopher D. Sogge

出版社Cambridge University Press

ISBN9781107120075

出版时间2016-01

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定价1627元

货号YB-70416

上书时间2024-07-02

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This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents H?rmander's propagation of singularities theorem and uses this to prove the Duistermaat–Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.