Fourier Integrals in Classical Analysis
(Book #210 in the Cambridge Tracts in Mathematics Series)
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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.
Format:Hardcover
Language:English
ISBN:1107120071
ISBN13:9781107120075
Release Date:April 2017
Publisher:Cambridge University Press
Length:348 Pages
Weight:1.50 lbs.
Dimensions:0.9" x 6.0" x 9.0"
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